A009486 - OEIS

%I #26 Feb 19 2020 13:39:23

%S 0,2,-8,-88,6592,-251488,4158592,551599232,-94759774208,9549823734272,

%T -506903275563008,-67623197282080768,30434079688615739392,

%U -6806476994628810661888,994937886379415577198592

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

%F 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

%t 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 *)

%o (Maxima)

%o 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 */

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997

%E Edited by _N. J. A. Sloane_, May 31 2008 at the suggestion of _R. J. Mathar_

%E Prior Mathematica program replaced by _Harvey P. Dale_, Feb 19 2020