A009484 From the expansion of sin(sin(x)*x).

0, 2, -4, -114, 3352, -35270, -2244012, 198654470, -8021832016, -150983244558, 67525484385580, -7526828271926018, 368068475511786696, 48206694242241834026, -16586068178557581107068, 2563355081796258270543990, -153878422314204916436611232

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

sin(x sin x) = Sum a(n) x^(2n)/(2n)!. - N. J. A. Sloane, Aug 28 2012

a(n) = sum(k=0..n, binomial(2*n,2*k+1)*(4^(-k)*sum(i=0..k, (2*i-2*k-1)^(2*n-2*k-1)*binomial(2*k+1,i)*(-1)^(n-i+k)))). - Vladimir Kruchinin, Jun 28 2011

Example

sin(sin(x)*x) = x^2-(1/6)*x^4-(19/120)*x^6+(419/5040)*x^8-(3527/362880)*x^10-(187001/39916800)*x^12+... - N. J. A. Sloane, Aug 28 2012

Mathematica

With[{nn=40}, Take[CoefficientList[Series[Sin[Sin[x]*x], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Aug 28 2012 *)

Prog

(Maxima)
a(n):=sum(binomial(2*n, 2*k+1)*(4^(-k)*sum((2*i-2*k-1)^(2*n-2*k-1)*binomial(2*k+1, i)*(-1)^(n-i+k), i, 0, k)), k, 0, n); /* Vladimir Kruchinin, Jun 28 2011 */

Crossrefs

Sequence in context: A289343 A018463 A132497 * A006314 A326204 A259381

Adjacent sequences: A009481 A009482 A009483 * A009485 A009486 A009487

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved