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A024337
Expansion of sinh(log(1+x))*log(1+x)/2.
0
0, 0, 1, -3, 13, -70, 447, -3297, 27576, -257904, 2667240, -30226680, 372517920, -4960668960, 70986162240, -1086347505600, 17705365171200, -306178316236800, 5599477712102400, -107980208561433600, 2189837602616832000
OFFSET
0,4
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
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 *)
CROSSREFS
Cf. A009575.
Sequence in context: A192209 A154677 A121586 * A001495 A284217 A213690
KEYWORD
sign
AUTHOR
EXTENSIONS
Extended with signs, Mar 1997
Prior Mathematica program replaced by Harvey P. Dale, Jan 16 2016
STATUS
approved