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 A009341 Expansion of e.g.f. log(1 + sin(x)*x), even powers only. 3
 0, 2, -16, 366, -17704, 1467370, -185815884, 33370050910, -8067253019536, 2526062494781394, -994534162338738580, 480859837194669214150, -280103496938395910686680, 193472520727526106582807226 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 FORMULA a(n) = 2*sum(k=1..2*n-1, binomial(2*n,k)*(k-1)!*(sum(i=0..k/2, (2*i-k)^(2*n-k)*binomial(k,i)*(-1)^(n-i+k-1)))/(2^k)). - Vladimir Kruchinin, Jun 28 2011 a(n) ~ (-1)^(n+1) * (2*n)! / (n*r^(2*n)), where r = 0.9320200293523439... (see A133867) is the root of the equation r*sinh(r)=1. - Vaclav Kotesovec, Apr 20 2014 MATHEMATICA With[{nn=30}, Take[CoefficientList[Series[Log[1+Sin[x]x], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Nov 27 2013 *) PROG (Maxima) a(n):=2*sum(binomial(2*n, k)*(k-1)!*(sum((2*i-k)^(2*n-k)*binomial(k, i)*(-1)^(n-i+k-1), i, 0, k/2))/(2^k), k, 1, 2*n-1); /* Vladimir Kruchinin, Jun 28 2011 */ CROSSREFS Cf. A133867. Sequence in context: A297095 A289972 A179472 * A015201 A227406 A068471 Adjacent sequences:  A009338 A009339 A009340 * A009342 A009343 A009344 KEYWORD sign AUTHOR EXTENSIONS Extended with signs by Olivier Gérard, Mar 15 1997 Previous Mathematica program replaced by Harvey P. Dale, Nov 27 2013 STATUS approved

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Last modified October 18 15:21 EDT 2019. Contains 328162 sequences. (Running on oeis4.)