A013369 Expansion of e.g.f. exp(sin(x)-sinh(x)).

1, 0, 0, -2, 0, 0, 40, -2, 0, -2240, 480, -2, 246400, -137280, 8320, -44844802, 51251200, -10325120, 12197916160, -24831206402, 11394406400, -4636033573760, 15296025241600, -13230894476802, 2348235343872000

Offset: 0

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

• sign

Examples

			1-2/3!*x^3+40/6!*x^6-2/7!*x^7-2240/9!*x^9...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..592

Crossrefs

Cf. A013025, A307978.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Sin[x]-Sinh[x]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, May 13 2020 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sin(x)-sinh(x)))) \\ Seiichi Manyama, Mar 17 2022

PARI

a(n) = if(n==0, 1, -2*sum(k=0, (n-3)\4, binomial(n-1, 4*k+2)*a(n-4*k-3))); \\ Seiichi Manyama, Mar 17 2022

Formula

a(0) = 1; a(n) = -2 * Sum_{k=0..floor((n-3)/4)} binomial(n-1,4*k+2) * a(n-4*k-3). - Seiichi Manyama, Mar 17 2022

Extensions

Definition clarified by Harvey P. Dale, May 13 2020