A356674 a(n) = n! * Sum_{k=0..n} k^(k*(n-k))/k!.
1, 2, 5, 25, 349, 19941, 4440391, 4382699203, 17687865017481, 356274213630958297, 33338407933090938442411, 16214021627369697901867402911, 43817834057167927861655409052462093, 595284492835035398061242850538179192931525
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..51
Programs
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Mathematica
Table[n!*(1 + Sum[k^(k*(n-k))/k!, {k, 1, n}]), {n, 0, 12}] (* Vaclav Kotesovec, Nov 27 2022 *) -
PARI
a(n) = n!*sum(k=0, n, k^(k*(n-k))/k!);
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^k*x)))))
Formula
E.g.f: Sum_{k>=0} x^k / (k! * (1 - k^k * x)).
log(a(n)) ~ n^2*log(n)/4 * (1 - log(2)/log(n) + 1/(4*log(n)^2)). - Vaclav Kotesovec, Nov 27 2022