rec1 := f[n+2]-4*f[n]*(n+1)/(n+2);
rec2 := f[4+n]+(96*n^3*f[n+1]-108*n^3*f[n+2]+9*n^3*f[n+3]+704*n^2*f[n+1]-900*n
^2*f[n+2]+84*n^2*f[n+3]+1664*n*f[n+1]-2468*n*f[n+2]+259*n*f[n+3]+1280*f[n+1]-\
2232*f[n+2]+264*f[n+3])/(n^2+8*n+16)/(3*n+7);
rec3 := f[n+6]+(5307120*n^8*f[n]-1505385*n^8*f[4+n]+10940832*n^8*f[n+1]+
4613112*n^8*f[n+2]-2449440*n^8*f[n+3]-71442*n^8*f[n+5]+161572320*n^7*f[n]-\
54862920*n^7*f[4+n]+349498800*n^7*f[n+1]+154282968*n^7*f[n+2]-85594320*n^7*f[n
+3]-2710827*n^7*f[n+5]+2101142160*n^6*f[n]-872672076*n^6*f[4+n]+4817164176*n^6
*f[n+1]+2241190080*n^6*f[n+2]-1302886296*n^6*f[n+3]-44881263*n^6*f[n+5]+
15185894880*n^5*f[n]-7913028498*n^5*f[4+n]+37377677352*n^5*f[n+1]+18466277640*
n^5*f[n+2]-11284127082*n^5*f[n+3]-423441408*n^5*f[n+5]+66389483680*n^4*f[n]-\
44736792299*n^4*f[4+n]+178377249016*n^4*f[n+1]+94375889012*n^4*f[n+2]-\
60826933104*n^4*f[n+3]-2489812810*n^4*f[n+5]+178613231680*n^3*f[n]-\
161475964162*n^3*f[4+n]+535508495312*n^3*f[n+1]+306303660908*n^3*f[n+2]-\
209004391390*n^3*f[n+3]-9342049921*n^3*f[n+5]+286253870240*n^2*f[n]-\
363378673696*n^2*f[4+n]+986458411952*n^2*f[n+1]+616437559400*n^2*f[n+2]-\
447123651220*n^2*f[n+3]-21840898009*n^2*f[n+5]+246754089920*n*f[n]-\
466106608416*n*f[4+n]+1018240007200*n*f[n+1]+703235185328*n*f[n+2]-\
544615939452*n*f[n+3]-29085469140*n*f[n+5]+85964985600*f[n]-260904024528*f[4+n
]+450400506240*f[n+1]+348147477312*f[n+2]-289246215216*f[n+3]-16889123100*f[n+
5])/(5103*n^8+201285*n^7+3456540*n^6+33749466*n^5+204915785*n^4+792207847*n^3+
1904280102*n^2+2601979092*n+1547183160);