A013025 Expansion of e.g.f. exp(sinh(x) + sin(x)).

1, 2, 4, 8, 16, 34, 88, 296, 1152, 4546, 17696, 72712, 343424, 1843170, 10274688, 56506024, 315332608, 1910439298, 12815815168, 90064672520, 629185325056, 4400756254114, 32422278027264, 258933905154856, 2168521319694336

Offset: 0

Author

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

Keywords

• nonn

Examples

			1+2*x+4/2!*x^2+8/3!*x^3+16/4!*x^4+34/5!*x^5...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A013369, A306347.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Sinh[x]+Sin[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 17 2011 *)

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-1)\4, binomial(n-1, 4*k)*a(n-4*k-1))); \\ Seiichi Manyama, Mar 17 2022

Formula

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