A073590 Expansion of e.g.f. exp(x) * log(1+x)/(1-x).

1, 3, 11, 44, 229, 1339, 9603, 75200, 690009, 6779803, 75792507, 896040188, 11811267389, 163229695459, 2478388484947, 39203092296480, 673698509829233, 12002969025435603, 230288108992819819, 4563243145806294636

Offset: 1

Author

Vladeta Jovovic, Aug 28 2002

Keywords

• nonn

Comments

Row sums of A073480.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..449

Crossrefs

Cf. A024167, A073480.

Programs

Mathematica

Rest[CoefficientList[Series[E^x*Log[1+x]/(1-x), {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jul 02 2015 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x)*log(1+x)/(1-x))) \\ Seiichi Manyama, Feb 20 2022

PARI

a(n) = sum(k=1, n, k!*binomial(n, k)*sum(j=1, k, (-1)^(j+1)/j)); \\ Seiichi Manyama, Feb 20 2022

Formula

a(n) ~ n! * exp(1) * log(2). - Vaclav Kotesovec, Jul 02 2015

a(n) = Sum_{k=1..n} k! * binomial(n,k) * Sum_{j=1..k} (-1)^(j+1)/j. - Seiichi Manyama, Feb 20 2022