A087301 a(n) = n!*Sum_{i=1..n-1} (-1)^(i+1)/i.

2, 3, 20, 70, 564, 3108, 30624, 230256, 2705760, 25771680, 352805760, 4067556480, 63651813120, 861371884800, 15176802816000, 235775183616000, 4620563523072000, 81032645804544000, 1748700390205440000

Offset: 2

Author

Vladeta Jovovic, Oct 20 2003

Keywords

• nonn

Comments

Stirling transform of A052882(n)=[0,2,9,52,375,...] is a(n+1)=[0,2,3,20,...]. - Michael Somos, Mar 04 2004

Crossrefs

Cf. A024167, A052881.

Programs

Mathematica

Rest[Table[n!Sum[(-1)^(i+1)/i,{i,n-1}],{n,20}]] (* Harvey P. Dale, Oct 24 2011 *)

PARI

a(n)=if(n<0,0,n!*polcoeff(log(1+x+x*O(x^n))*x/(1-x),n))

Formula

E.g.f.: x*log(1+x)/(1-x). a(n) = 1/2*(-1)^n*n!*(2*(-1)^n*log(2)+Psi(1/2+1/2*n)-Psi(1/2*n)).

a(n) ~ n! * log(2). - Vaclav Kotesovec, Jul 01 2018