A024337 Expansion of sinh(log(1+x))*log(1+x)/2.

0, 0, 1, -3, 13, -70, 447, -3297, 27576, -257904, 2667240, -30226680, 372517920, -4960668960, 70986162240, -1086347505600, 17705365171200, -306178316236800, 5599477712102400, -107980208561433600, 2189837602616832000

Offset: 0

Author

R. H. Hardin

Keywords

• sign

Crossrefs

Cf. A009575.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Sinh[Log[1+x]]*Log[1+x]/2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 16 2016 *)

Formula

a(n) = (-1)^n*(n!*h(n)+(n-2)!)/4, n>1, where h(n) = Sum_{k=1..n} 1/k. - Gary Detlefs, Jul 31 2010

Conjecture: a(n) = Sum_{k=0..n/2} Stirling1(n,2*k)*k. - Benedict W. J. Irwin, Oct 14 2016

Extensions

Extended with signs, Mar 1997

Prior Mathematica program replaced by Harvey P. Dale, Jan 16 2016