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A351182
a(n) = Sum_{k=0..n} k^(2*k) * Stirling1(n,k).
4
1, 1, 15, 683, 61332, 9135004, 2035708760, 634172615600, 263166948202080, 140322186951905736, 93484350581344936344, 76095870609142447018152, 74311960997497053384537408, 85748280952260853814490688656
OFFSET
0,3
FORMULA
E.g.f.: Sum_{k>=0} (k^2 * log(1+x))^k / k!.
a(n) ~ exp(-exp(-2)/2) * n^(2*n). - Vaclav Kotesovec, Feb 18 2022
PROG
(PARI) a(n) = sum(k=0, n, k^(2*k)*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*log(1+x))^k/k!)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 04 2022
STATUS
approved