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A300488

a(n) = n! * [x^n] -exp(n*x)*log(1 - x)/(1 - x).

0, 1, 7, 65, 770, 11149, 191124, 3788469, 85281552, 2149582761, 59983774240, 1835925702137, 61157508893568, 2202760340194517, 85303050939131648, 3534478528925155725, 156026612737389987840, 7310587974761946511761, 362356607517279564386304, 18943214212273585171456753

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=1..n} n^(n-k)*binomial(n,k)*k!*H(k), where H(k) is the k-th harmonic number.

EXAMPLE

The table of coefficients of x^k in expansion of e.g.f. -exp(n*x)*log(1 - x)/(1 - x) begins:

n = 0: (0), 1, 3, 11, 50, 274, ...

n = 1: 0, (1), 5, 23, 116, 669, ...