A092692 Expansion of e.g.f. -log(1-x)/(1-x^2).

0, 1, 1, 8, 18, 184, 660, 8448, 42000, 648576, 4142880, 74972160, 586776960, 12174658560, 113020427520, 2643856588800, 28432576972800, 740051782041600, 9056055981772800, 259500083163955200, 3562946373482496000

Offset: 0

Author

Michael Somos, Mar 04 2004

Keywords

• nonn

Comments

Stirling transform of (-1)^n*a(n-1)=[0,1,-1,8,-18,...] is A052882(n-1)=[0,1,2,9,52,...].

Links

• G. C. Greubel, Table of n, a(n) for n = 0..448

Programs

Mathematica

nmax = 20; CoefficientList[Series[-Log[1-x]/(1-x^2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 01 2018 *)

PARI

a(n)=if(n<0,0,n!*polcoeff(-log(1-x+x*O(x^n))/(1-x^2),n))

PARI

{a(n)=if(n<0, 0, n!*sum(k=1, n, ((n-k+1)%2)/k))} /* Michael Somos, Sep 19 2006 */

Formula

E.g.f.: -log(1-x)/(1-x^2).

a(n) = n!*Sum_{k=1..n} (-1)^(n-k)*Harmonic(k). - Vladeta Jovovic, Aug 14 2005

a(n) ~ n! * (log(n) + gamma - (-1)^n * log(2)) / 2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 01 2018