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A354262
Expansion of e.g.f. 1/sqrt(1 + 8 * log(1-x)).
2
1, 4, 52, 1112, 33192, 1272576, 59607552, 3298935552, 210638509824, 15241340093952, 1232504690492928, 110154484622208000, 10782300230031713280, 1147157496053856645120, 131810751499551281786880, 16266976762439018716323840, 2145960434809665656603320320
OFFSET
0,2
FORMULA
E.g.f.: Sum_{k>=0} binomial(2*k,k) * (-2 * log(1-x))^k.
a(n) = Sum_{k=0..n} 2^k * (2*k)! * |Stirling1(n,k)|/k!.
a(n) ~ n^n / (2 * (exp(1/8)-1)^(n + 1/2) * exp(7*n/8)). - Vaclav Kotesovec, Jun 04 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+8*log(1-x))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(-2*log(1-x))^k)))
(PARI) a(n) = sum(k=0, n, 2^k*(2*k)!*abs(stirling(n, k, 1))/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 21 2022
STATUS
approved