#The list of the first, 35, even diagonal moments of the trivariate normal dis\ # trubution with covariance matrix # # # [ 1 c12 c13] [ ] [c12 1 c23] [ ] [c13 c23 1 ] are L:= [8*c12*c13*c23+2*c12^2+2*c13^2+2*c23^2+1, 1728*c12^2*c13^2*c23^2+1152*c12^3*c13 *c23+1152*c12*c13^3*c23+1152*c12*c13*c23^3+72*c12^4+864*c12^2*c13^2+864*c12^2* c23^2+72*c13^4+864*c13^2*c23^2+72*c23^4+1728*c12*c13*c23+216*c12^2+216*c13^2+ 216*c23^2+27, 1728000*c12^3*c13^3*c23^3+1944000*c12^4*c13^2*c23^2+1944000*c12^2 *c13^4*c23^2+1944000*c12^2*c13^2*c23^4+388800*c12^5*c13*c23+2592000*c12^3*c13^3 *c23+2592000*c12^3*c13*c23^3+388800*c12*c13^5*c23+2592000*c12*c13^3*c23^3+ 388800*c12*c13*c23^5+10800*c12^6+486000*c12^4*c13^2+486000*c12^4*c23^2+486000* c12^2*c13^4+5832000*c12^2*c13^2*c23^2+486000*c12^2*c23^4+10800*c13^6+486000*c13 ^4*c23^2+486000*c13^2*c23^4+10800*c23^6+1944000*c12^3*c13*c23+1944000*c12*c13^3 *c23+1944000*c12*c13*c23^3+81000*c12^4+729000*c12^2*c13^2+729000*c12^2*c23^2+ 81000*c13^4+729000*c13^2*c23^2+81000*c23^4+729000*c12*c13*c23+60750*c12^2+60750 *c13^2+60750*c23^2+3375, 4741632000*c12^4*c13^4*c23^4+7586611200*c12^5*c13^3* c23^3+7586611200*c12^3*c13^5*c23^3+7586611200*c12^3*c13^3*c23^5+2844979200*c12^ 6*c13^2*c23^2+14224896000*c12^4*c13^4*c23^2+14224896000*c12^4*c13^2*c23^4+ 2844979200*c12^2*c13^6*c23^2+14224896000*c12^2*c13^4*c23^4+2844979200*c12^2*c13 ^2*c23^6+270950400*c12^7*c13*c23+5689958400*c12^5*c13^3*c23+5689958400*c12^5* c13*c23^3+5689958400*c12^3*c13^5*c23+37933056000*c12^3*c13^3*c23^3+5689958400* c12^3*c13*c23^5+270950400*c12*c13^7*c23+5689958400*c12*c13^5*c23^3+5689958400* c12*c13^3*c23^5+270950400*c12*c13*c23^7+4233600*c12^8+474163200*c12^6*c13^2+ 474163200*c12^6*c23^2+1778112000*c12^4*c13^4+21337344000*c12^4*c13^2*c23^2+ 1778112000*c12^4*c23^4+474163200*c12^2*c13^6+21337344000*c12^2*c13^4*c23^2+ 21337344000*c12^2*c13^2*c23^4+474163200*c12^2*c23^6+4233600*c13^8+474163200*c13 ^6*c23^2+1778112000*c13^4*c23^4+474163200*c13^2*c23^6+4233600*c23^8+2844979200* c12^5*c13*c23+14224896000*c12^3*c13^3*c23+14224896000*c12^3*c13*c23^3+ 2844979200*c12*c13^5*c23+14224896000*c12*c13^3*c23^3+2844979200*c12*c13*c23^5+ 59270400*c12^6+1778112000*c12^4*c13^2+1778112000*c12^4*c23^2+1778112000*c12^2* c13^4+16003008000*c12^2*c13^2*c23^2+1778112000*c12^2*c23^4+59270400*c13^6+ 1778112000*c13^4*c23^2+1778112000*c13^2*c23^4+59270400*c23^6+3556224000*c12^3* c13*c23+3556224000*c12*c13^3*c23+3556224000*c12*c13*c23^3+111132000*c12^4+ 889056000*c12^2*c13^2+889056000*c12^2*c23^2+111132000*c13^4+889056000*c13^2*c23 ^2+111132000*c23^4+592704000*c12*c13*c23+37044000*c12^2+37044000*c13^2+37044000 *c23^2+1157625, 27653197824000*c12^5*c13^5*c23^5+57610828800000*c12^6*c13^4*c23 ^4+57610828800000*c12^4*c13^6*c23^4+57610828800000*c12^4*c13^4*c23^6+ 32920473600000*c12^7*c13^3*c23^3+138265989120000*c12^5*c13^5*c23^3+ 138265989120000*c12^5*c13^3*c23^5+32920473600000*c12^3*c13^7*c23^3+ 138265989120000*c12^3*c13^5*c23^5+32920473600000*c12^3*c13^3*c23^7+ 6172588800000*c12^8*c13^2*c23^2+86416243200000*c12^6*c13^4*c23^2+86416243200000 *c12^6*c13^2*c23^4+86416243200000*c12^4*c13^6*c23^2+432081216000000*c12^4*c13^4 *c23^4+86416243200000*c12^4*c13^2*c23^6+6172588800000*c12^2*c13^8*c23^2+ 86416243200000*c12^2*c13^6*c23^4+86416243200000*c12^2*c13^4*c23^6+6172588800000 *c12^2*c13^2*c23^8+342921600000*c12^9*c13*c23+16460236800000*c12^7*c13^3*c23+ 16460236800000*c12^7*c13*c23^3+51849745920000*c12^5*c13^5*c23+345664972800000* c12^5*c13^3*c23^3+51849745920000*c12^5*c13*c23^5+16460236800000*c12^3*c13^7*c23 +345664972800000*c12^3*c13^5*c23^3+345664972800000*c12^3*c13^3*c23^5+ 16460236800000*c12^3*c13*c23^7+342921600000*c12*c13^9*c23+16460236800000*c12* c13^7*c23^3+51849745920000*c12*c13^5*c23^5+16460236800000*c12*c13^3*c23^7+ 342921600000*c12*c13*c23^9+3429216000*c12^10+771573600000*c12^8*c13^2+ 771573600000*c12^8*c23^2+7201353600000*c12^6*c13^4+86416243200000*c12^6*c13^2* c23^2+7201353600000*c12^6*c23^4+7201353600000*c12^4*c13^6+324060912000000*c12^4 *c13^4*c23^2+324060912000000*c12^4*c13^2*c23^4+7201353600000*c12^4*c23^6+ 771573600000*c12^2*c13^8+86416243200000*c12^2*c13^6*c23^2+324060912000000*c12^2 *c13^4*c23^4+86416243200000*c12^2*c13^2*c23^6+771573600000*c12^2*c23^8+ 3429216000*c13^10+771573600000*c13^8*c23^2+7201353600000*c13^6*c23^4+ 7201353600000*c13^4*c23^6+771573600000*c13^2*c23^8+3429216000*c23^10+ 6172588800000*c12^7*c13*c23+86416243200000*c12^5*c13^3*c23+86416243200000*c12^5 *c13*c23^3+86416243200000*c12^3*c13^5*c23+432081216000000*c12^3*c13^3*c23^3+ 86416243200000*c12^3*c13*c23^5+6172588800000*c12*c13^7*c23+86416243200000*c12* c13^5*c23^3+86416243200000*c12*c13^3*c23^5+6172588800000*c12*c13*c23^7+ 77157360000*c12^8+5401015200000*c12^6*c13^2+5401015200000*c12^6*c23^2+ 18003384000000*c12^4*c13^4+162030456000000*c12^4*c13^2*c23^2+18003384000000*c12 ^4*c23^4+5401015200000*c12^2*c13^6+162030456000000*c12^2*c13^4*c23^2+ 162030456000000*c12^2*c13^2*c23^4+5401015200000*c12^2*c23^6+77157360000*c13^8+ 5401015200000*c13^6*c23^2+18003384000000*c13^4*c23^4+5401015200000*c13^2*c23^6+ 77157360000*c23^8+16203045600000*c12^5*c13*c23+72013536000000*c12^3*c13^3*c23+ 72013536000000*c12^3*c13*c23^3+16203045600000*c12*c13^5*c23+72013536000000*c12* c13^3*c23^3+16203045600000*c12*c13*c23^5+270050760000*c12^6+6751269000000*c12^4 *c13^2+6751269000000*c12^4*c23^2+6751269000000*c12^2*c13^4+54010152000000*c12^2 *c13^2*c23^2+6751269000000*c12^2*c23^4+270050760000*c13^6+6751269000000*c13^4* c23^2+6751269000000*c13^2*c23^4+270050760000*c23^6+9001692000000*c12^3*c13*c23+ 9001692000000*c12*c13^3*c23+9001692000000*c12*c13*c23^3+225042300000*c12^4+ 1687817250000*c12^2*c13^2+1687817250000*c12^2*c23^2+225042300000*c13^4+ 1687817250000*c13^2*c23^2+225042300000*c23^4+843908625000*c12*c13*c23+ 42195431250*c12^2+42195431250*c13^2+42195431250*c23^2+843908625, 294451250429952000*c12^6*c13^6*c23^6+757160358248448000*c12^7*c13^5*c23^5+ 757160358248448000*c12^5*c13^7*c23^5+757160358248448000*c12^5*c13^5*c23^7+ 591531529881600000*c12^8*c13^4*c23^4+2208384378224640000*c12^6*c13^6*c23^4+ 2208384378224640000*c12^6*c13^4*c23^6+591531529881600000*c12^4*c13^8*c23^4+ 2208384378224640000*c12^4*c13^6*c23^6+591531529881600000*c12^4*c13^4*c23^8+ 175268601446400000*c12^9*c13^3*c23^3+1892900895621120000*c12^7*c13^5*c23^3+ 1892900895621120000*c12^7*c13^3*c23^5+1892900895621120000*c12^5*c13^7*c23^3+ 7950183761608704000*c12^5*c13^5*c23^5+1892900895621120000*c12^5*c13^3*c23^7+ 175268601446400000*c12^3*c13^9*c23^3+1892900895621120000*c12^3*c13^7*c23^5+ 1892900895621120000*c12^3*c13^5*c23^7+175268601446400000*c12^3*c13^3*c23^9+ 19717717662720000*c12^10*c13^2*c23^2+591531529881600000*c12^8*c13^4*c23^2+ 591531529881600000*c12^8*c13^2*c23^4+1656288283668480000*c12^6*c13^6*c23^2+ 8281441418342400000*c12^6*c13^4*c23^4+1656288283668480000*c12^6*c13^2*c23^6+ 591531529881600000*c12^4*c13^8*c23^2+8281441418342400000*c12^4*c13^6*c23^4+ 8281441418342400000*c12^4*c13^4*c23^6+591531529881600000*c12^4*c13^2*c23^8+ 19717717662720000*c12^2*c13^10*c23^2+591531529881600000*c12^2*c13^8*c23^4+ 1656288283668480000*c12^2*c13^6*c23^6+591531529881600000*c12^2*c13^4*c23^8+ 19717717662720000*c12^2*c13^2*c23^10+717007915008000*c12^11*c13*c23+ 65725725542400000*c12^9*c13^3*c23+65725725542400000*c12^9*c13*c23^3+ 473225223905280000*c12^7*c13^5*c23+3154834826035200000*c12^7*c13^3*c23^3+ 473225223905280000*c12^7*c13*c23^5+473225223905280000*c12^5*c13^7*c23+ 9937729702010880000*c12^5*c13^5*c23^3+9937729702010880000*c12^5*c13^3*c23^5+ 473225223905280000*c12^5*c13*c23^7+65725725542400000*c12^3*c13^9*c23+ 3154834826035200000*c12^3*c13^7*c23^3+9937729702010880000*c12^3*c13^5*c23^5+ 3154834826035200000*c12^3*c13^3*c23^7+65725725542400000*c12^3*c13*c23^9+ 717007915008000*c12*c13^11*c23+65725725542400000*c12*c13^9*c23^3+ 473225223905280000*c12*c13^7*c23^5+473225223905280000*c12*c13^5*c23^7+ 65725725542400000*c12*c13^3*c23^9+717007915008000*c12*c13*c23^11+4979221632000* c12^12+1971771766272000*c12^10*c13^2+1971771766272000*c12^10*c23^2+ 36970720617600000*c12^8*c13^4+443648647411200000*c12^8*c13^2*c23^2+ 36970720617600000*c12^8*c23^4+92016015759360000*c12^6*c13^6+4140720709171200000 *c12^6*c13^4*c23^2+4140720709171200000*c12^6*c13^2*c23^4+92016015759360000*c12^ 6*c23^6+36970720617600000*c12^4*c13^8+4140720709171200000*c12^4*c13^6*c23^2+ 15527702659392000000*c12^4*c13^4*c23^4+4140720709171200000*c12^4*c13^2*c23^6+ 36970720617600000*c12^4*c23^8+1971771766272000*c12^2*c13^10+443648647411200000* c12^2*c13^8*c23^2+4140720709171200000*c12^2*c13^6*c23^4+4140720709171200000*c12 ^2*c13^4*c23^6+443648647411200000*c12^2*c13^2*c23^8+1971771766272000*c12^2*c23^ 10+4979221632000*c13^12+1971771766272000*c13^10*c23^2+36970720617600000*c13^8* c23^4+92016015759360000*c13^6*c23^6+36970720617600000*c13^4*c23^8+ 1971771766272000*c13^2*c23^10+4979221632000*c23^12+19717717662720000*c12^9*c13* c23+591531529881600000*c12^7*c13^3*c23+591531529881600000*c12^7*c13*c23^3+ 1656288283668480000*c12^5*c13^5*c23+8281441418342400000*c12^5*c13^3*c23^3+ 1656288283668480000*c12^5*c13*c23^5+591531529881600000*c12^3*c13^7*c23+ 8281441418342400000*c12^3*c13^5*c23^3+8281441418342400000*c12^3*c13^3*c23^5+ 591531529881600000*c12^3*c13*c23^7+19717717662720000*c12*c13^9*c23+ 591531529881600000*c12*c13^7*c23^3+1656288283668480000*c12*c13^5*c23^5+ 591531529881600000*c12*c13^3*c23^7+19717717662720000*c12*c13*c23^9+ 164314313856000*c12^10+22182432370560000*c12^8*c13^2+22182432370560000*c12^8* c23^2+172530029548800000*c12^6*c13^4+1552770265939200000*c12^6*c13^2*c23^2+ 172530029548800000*c12^6*c23^4+172530029548800000*c12^4*c13^6+ 5175900886464000000*c12^4*c13^4*c23^2+5175900886464000000*c12^4*c13^2*c23^4+ 172530029548800000*c12^4*c23^6+22182432370560000*c12^2*c13^8+ 1552770265939200000*c12^2*c13^6*c23^2+5175900886464000000*c12^2*c13^4*c23^4+ 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