A009321 E.g.f. log(1 + log(1+x)*exp(x)).

0, 1, 0, 1, -5, 23, -129, 894, -7202, 65365, -661763, 7412348, -91009060, 1214988851, -17522921545, 271538506004, -4499710415184, 79404970485241, -1486680068450391, 29435486083635796, -614519419914446388

Offset

0,5

Links

Table of n, a(n) for n=0..20.

Formula

a(n)=sum(k=1..n, ((-1)^(k-1)*(k-1)!*sum(i=0..n-k, binomial(n,i)*(k^i*stirling1(n-i,k))))). - Vladimir Kruchinin, Jun 14 2011

a(n) ~ (n-1)! * (-1)^(n+1) / (1-exp(-r))^n, where r = 2.5051123308583601790988703653235907822189... is the root of the equation exp(-1 + exp(-r))*r = 1. - Vaclav Kotesovec, Jan 24 2015

Mathematica

CoefficientList[Series[Log[1 + E^x*Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

Prog

(Maxima)
a(n):=sum(((-1)^(k-1)*(k-1)!*sum(binomial(n, i)*(k^i*stirling1(n-i, k)), i, 0, n-k)), k, 1, n); /* Vladimir Kruchinin, Jun 14 2011 */

Crossrefs

Sequence in context: A020032 A293088 A186755 * A078509 A239820 A077240

Adjacent sequences: A009318 A009319 A009320 * A009322 A009323 A009324

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved