A377396 - OEIS

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A377396

Expansion of e.g.f. (1 + log(1+x))^3.

1, 3, 3, -6, 12, -18, -66, 1320, -15504, 172200, -1965384, 23636016, -301995216, 4107704832, -59444810496, 913681776384, -14882950782720, 256316144325120, -4656243408560640, 89018690328990720, -1787202802367585280, 37603576325804544000, -827595379013405184000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = Sum_{k=0..3} k! * binomial(3,k) * Stirling1(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (4 * k/n - 1) * (k-1)! * binomial(n,k) * a(n-k).

PROG

(PARI) a(n) = sum(k=0, 3, k!*binomial(3, k)*stirling(n, k, 1));

CROSSREFS

Cf. A377397.