A377395 Expansion of e.g.f. (1 - log(1-x))^4.

1, 4, 16, 68, 324, 1776, 11208, 80664, 654600, 5926080, 59283552, 649972704, 7754418528, 100047107520, 1388392475328, 20625806330496, 326648173136256, 5494182397387776, 97821610887785472, 1838137437962182656, 36354781509406470144, 754959568444846387200

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..449

Formula

a(n) = Sum_{k=0..4} k! * binomial(4,k) * |Stirling1(n,k)|.

a(0) = 1; a(n) = Sum_{k=1..n} (5 * k/n - 1) * (k-1)! * binomial(n,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, 4, k!*binomial(4, k)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A052517, A052748, A052753.

Sequence in context: A228950 A354121 A297203 * A231297 A339045 A341255

Adjacent sequences: A377392 A377393 A377394 * A377396 A377397 A377398

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 27 2024

Status

approved