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A354674
a(n) = Sum_{k=0..n} k! * k^(k+n) * |Stirling1(n,k)|.
0
1, 1, 33, 4568, 1653010, 1236180194, 1657339714418, 3620923498508952, 12037504737979759944, 57827877567223173191712, 385581993722741959459382352, 3454851578510897594456017095504, 40509304222426523176427339597382336
OFFSET
0,3
FORMULA
E.g.f.: Sum_{k>=0} (-k * log(1 - k*x))^k.
PROG
(PARI) a(n) = sum(k=0, n, k!*k^(k+n)*abs(stirling(n, k, 1)));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k*log(1-k*x))^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 02 2022
STATUS
approved