OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..370
FORMULA
a(n) ~ c * 12^n * n^(n+1/2) / (exp(n) * Pi^(2*n)), where c = -12 / (Pi^(3/2) * exp(5*Pi^2/24)) = -0.275723765924812729... - Vaclav Kotesovec, Dec 01 2014, updated Aug 22 2017
MATHEMATICA
nmax = 20; aa = ConstantArray[0, nmax]; aa[[1]] = 1; Do[AGF = 1+Sum[aa[[n]]*x^n, {n, 1, j-1}]+koef*x^j; sol=Solve[SeriesCoefficient[Sum[Product[(1-1/AGF^(2m-1)), {m, 1, k}], {k, 1, j}], {x, 0, j}]==0, koef][[1]]; aa[[j]]=koef/.sol[[1]], {j, 2, nmax}]; Flatten[{1, aa}]
PROG
(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0);
A[#A]=-polcoeff(sum(m=1, #A, prod(k=1, m, 1-1/Ser(A)^(2*k-1))), #A-1)); A[n+1]}
for(n=0, 25, print1(a(n), ", ")) \\ Vaclav Kotesovec, Mar 17 2024, after Paul D. Hanna
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Dec 01 2014
STATUS
approved