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A356806
a(n) = Sum_{k=0..n} (k*n-1)^(n-k) * binomial(n,k).
6
1, 0, 4, 27, 448, 10625, 344736, 14437213, 753991680, 47974773393, 3650824000000, 326917384798301, 33956137832546304, 4041303651931462969, 545552768347831566336, 82828479894303251953125, 14040577418634835164921856, 2640293357854435329683551265
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * [x^n] exp( x * (exp(n * x) - 1) ).
a(n) = n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling2(n-k,k)/(n-k)!.
a(n) = [x^n] Sum_{k>=0} x^k / (1 - (n*k-1)*x)^(k+1).
PROG
(PARI) a(n) = sum(k=0, n, (k*n-1)^(n-k)*binomial(n, k));
(PARI) a(n) = n!*sum(k=0, n\2, n^(n-k)*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 29 2022
STATUS
approved