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A336949
a(n) = n! * [x^n] 1 / (exp(-n*x) - x).
3
1, 2, 14, 195, 4440, 147745, 6698448, 394852577, 29250137472, 2652483234033, 288363456748800, 36952298766628465, 5504130616452258816, 941845623036360908489, 183298110723156455921664, 40221612394630225987208625, 9876429434585097671993032704
OFFSET
0,2
FORMULA
a(n) = n! * Sum_{k=0..n} (n * (n-k+1))^k / k!.
MATHEMATICA
Table[n! SeriesCoefficient[1/(Exp[-n x] - x), {x, 0, n}], {n, 0, 16}]
Join[{1}, Table[n! Sum[(n (n - k + 1))^k/k!, {k, 0, n}], {n, 1, 16}]]
PROG
(PARI) a(n)={n!*polcoef(1/(exp(-n*x + O(x*x^n)) - x), n)} \\ Andrew Howroyd, Aug 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 08 2020
STATUS
approved