OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..n} (-2)^(n-k) * (Product_{j=0..k-1} (-2*j+1)) * Stirling1(n,k).
a(n) ~ n! * 2^(n-1) / (sqrt(log(n)) * n) * (1 - (gamma + 1)/(2*log(n))), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 05 2022
MATHEMATICA
m = 20; Range[0, m]! * CoefficientList[Series[(1 - Log[1 - 2*x])^(1/2), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(1-log(1-2*x))))
(PARI) a(n) = sum(k=0, n, (-2)^(n-k)*prod(j=0, k-1, -2*j+1)*stirling(n, k, 1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2022
STATUS
approved