A009486 sin(sin(x)*sin(x)) = 2/2!*x^2 - 8/4!*x^4 - 88/6!*x^6 + 6592/8!*x^8 - ...

0, 2, -8, -88, 6592, -251488, 4158592, 551599232, -94759774208, 9549823734272, -506903275563008, -67623197282080768, 30434079688615739392, -6806476994628810661888, 994937886379415577198592

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Sin[Sin[x]^2] , {x, 0, nn}], x] Range[ 0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Feb 19 2020 *)

Prog

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

Crossrefs

Sequence in context: A054955 A012299 A012295 * A110384 A153887 A131349

Adjacent sequences: A009483 A009484 A009485 * A009487 A009488 A009489

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Edited by N. J. A. Sloane, May 31 2008 at the suggestion of R. J. Mathar

Prior Mathematica program replaced by Harvey P. Dale, Feb 19 2020

Status

approved