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

Author

R. H. Hardin

Keywords

• sign
• easy

Programs

Mathematica

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

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 */

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997