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%I #17 Aug 31 2018 00:24:46
%S 0,1,1,8,18,184,660,8448,42000,648576,4142880,74972160,586776960,
%T 12174658560,113020427520,2643856588800,28432576972800,
%U 740051782041600,9056055981772800,259500083163955200,3562946373482496000
%N Expansion of e.g.f. -log(1-x)/(1-x^2).
%C Stirling transform of (-1)^n*a(n-1)=[0,1,-1,8,-18,...] is A052882(n-1)=[0,1,2,9,52,...].
%H G. C. Greubel, <a href="/A092692/b092692.txt">Table of n, a(n) for n = 0..448</a>
%F E.g.f.: -log(1-x)/(1-x^2).
%F a(n) = n!*Sum_{k=1..n} (-1)^(n-k)*Harmonic(k). - _Vladeta Jovovic_, Aug 14 2005
%F a(n) ~ n! * (log(n) + gamma - (-1)^n * log(2)) / 2, where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 01 2018
%t nmax = 20; CoefficientList[Series[-Log[1-x]/(1-x^2), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Jul 01 2018 *)
%o (PARI) a(n)=if(n<0,0,n!*polcoeff(-log(1-x+x*O(x^n))/(1-x^2),n))
%o (PARI) {a(n)=if(n<0, 0, n!*sum(k=1, n, ((n-k+1)%2)/k))} /* _Michael Somos_, Sep 19 2006 */
%K nonn
%O 0,4
%A _Michael Somos_, Mar 04 2004
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