#OK to post
#Yuxuan Yang, March 28th, Assignment 16

with(combinat):
#1



ComputCons:=proc(F, P, n, d) local total,p,f,k,fq:
Digits:=d+3:
fq:=F/subs(n=n-1,F):
total := 0:
f := evalf(subs(n=0,F)):
p:=1/f:
    for k from 1 while evalf(abs(f*p))>evalf(10^(-d)) do
        f := evalf(-1 * f * subs(n=k,fq)):
        p := evalf(subs(n=k,P)):
        total := total + f*p:
    od:
Digits:=d:
evalf(total):
end:


#ComputCons(n^3 + 1, 3^n/binomial(2*n, n)^10, n, 10000)
#Digits:=10000:evalf(add((-1)^n*(n^3 + 1)*3^n/binomial(2*n, n)^10, n = 1 .. 1900))

#they give the same results



#2
#seq(nops(LT(i, i)), i = 1 .. 6) gives 1, 0, 1, 0, 4, 236
#Not found in OEIS

#3#4 were sent in another pdf file.