A377394 Expansion of e.g.f. (1 - log(1-x))^3.

1, 3, 9, 30, 120, 582, 3354, 22488, 172320, 1487208, 14284296, 151179696, 1748521296, 21945019392, 297077918976, 4315269544704, 66952906801920, 1105127533048320, 19337110495511040, 357542547031249920, 6965984564179246080, 142638952766943744000, 3062533108375448064000

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..450

Formula

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

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

Prog

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

Crossrefs

Cf. A052517, A052748.

Sequence in context: A292758 A297198 A297202 * A370439 A003604 A357615

Adjacent sequences: A377391 A377392 A377393 * A377395 A377396 A377397

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 27 2024

Status

approved