OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..375
FORMULA
Sum_{n>=0} (1+x)^(n*(n+1)) / (1 + (1+x)^n)^(n+1).
a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = 3.1610886538654288138301722... and c = 0.8785394171057422507960514834733179025314463... - Vaclav Kotesovec, Oct 04 2020
EXAMPLE
G.f.: A(x) = 1 + 2*x + 10*x^2 + 82*x^3 + 928*x^4 + 13406*x^5 + 235690*x^6 + 4883702*x^7 + 116548222*x^8 + ...
PROG
(PARI) {a(n) = polcoeff( sum(k=0, n, ((1+x +x*O(x^n))^(k+1) - 1)^k), n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) /* From e.g.f. infinite series: */
\p200 \\ set precision
{A = Vec(round( sum(n=0, 600, 1./(1 + (1+x +O(x^26))^(-n))^(n+1)) ))}
for(n=0, #A-1, print1(A[n+1], ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 04 2018
STATUS
approved