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A247482
G.f. A(x) satisfies: x = Sum_{n>=1} Product_{k=1..n} (1 - 1/A(x)^(2*k-1)).
3
1, 1, -2, 1, -3, -18, -124, -1174, -12150, -141536, -1816780, -25461723, -386593670, -6320496592, -110711177281, -2068814967831, -41089562943757, -864563028340432, -19214971769126974, -449887669808788433, -11069673481210168218, -285604488897863640237
OFFSET
0,3
LINKS
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
Cf. A247481 (exponent=1), A249934 (exponent=3), A214692 (exponent=4), A247480 (exponent=5), A214693 (exponent=6), A214694 (exponent=8), A214695 (exponent=10).
Sequence in context: A132950 A197190 A376084 * A156364 A106169 A319493
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Dec 01 2014
STATUS
approved