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A009595 Expansion of e.g.f. sinh(sin(x)*x), even powers only. 2
0, 2, -4, 126, -3368, 95770, -4408812, 265489238, -18154718416, 1485105153714, -146642787086420, 16695614806747822, -2147275569222109944, 312504772665433249226, -51165984479663630172988, 9306072483765112492581510 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n-1} binomial(2*n,2*k+1)*(2^(-2*k)*Sum_{i=0..k} (2*i -2*k-1)^(2*n-2*k-1)*binomial(2*k+1,i)*(-1)^(n-i)). - Vladimir Kruchinin, Jun 29 2011
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Sinh[Sin[x]*x], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 2]] (* G. C. Greubel, Jan 30 2018 *)
PROG
(Maxima)
a(n):=sum(binomial(2*n, 2*k+1)*(2^(-2*k)*sum((2*i-2*k-1)^(2*n-2*k-1)*binomial(2*k+1, i)*(-1)^(n-i), i, 0, k)), k, 0, n-1); /* Vladimir Kruchinin, Jun 29 2011 */
(PARI) x='x+O('x^50); v=Vec(serlaplace(sinh(x*sin(x)))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Jan 30 2018 *)
CROSSREFS
Sequence in context: A326204 A259381 A333621 * A018493 A046035 A134710
KEYWORD
sign
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved

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Last modified June 16 13:05 EDT 2024. Contains 373429 sequences. (Running on oeis4.)