A351180 a(n) = Sum_{k=0..n} k^(k+n) * Stirling1(n,k).
1, 1, 15, 635, 53112, 7367444, 1529130770, 443685287576, 171495189203456, 85174828026304824, 52856314387144232184, 40077340463437963801752, 36457068309928364981668848, 39186634107857517367884040632
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := Sum[k^(k + n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 14, 0] (* Amiram Eldar, Feb 04 2022 *) -
PARI
a(n) = sum(k=0, n, k^(k+n)*stirling(n, k, 1));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+k*x))^k/k!)))
Formula
E.g.f.: Sum_{k>=0} (k * log(1 + k*x))^k / k!.
a(n) ~ c * d^n * n^(2*n), where d = 0.9315722818790917570256960813246568629715677803436281996798798428122211769... and c = 1.07238575181275524934156216072811545518508724720534339814911465361... - Vaclav Kotesovec, Feb 18 2022