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A351138
a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * k^(k*n) * Stirling1(n,k).
4
1, 1, 33, 118484, 103098352618, 35763050751038414134, 7426387531294394110580641088438, 1294894837982331434068068403253026516109577144, 253092742000650212462862632240661689524832716838851180353875064
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Sum_{k>=0} (-log(1 - k^k*x))^k.
a(n) ~ n! * n^(n^2). - Vaclav Kotesovec, Feb 03 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[(-1)^(n - k) * k! * k^(k*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 9, 0] (* Amiram Eldar, Feb 02 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k!*k^(k*n)*stirling(n, k, 1));
(PARI) my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-log(1-k^k*x))^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 02 2022
STATUS
approved