A009341 Expansion of e.g.f. log(1 + sin(x)*x), even powers only.

0, 2, -16, 366, -17704, 1467370, -185815884, 33370050910, -8067253019536, 2526062494781394, -994534162338738580, 480859837194669214150, -280103496938395910686680, 193472520727526106582807226

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 * A366396 A015201 A227406

Adjacent sequences: A009338 A009339 A009340 * A009342 A009343 A009344

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Nov 27 2013

Status

approved