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

0,2

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A013369, A306347.

Sequence in context: A166354 A336009 A180207 * A034339 A244519 A247293

Adjacent sequences: A013022 A013023 A013024 * A013026 A013027 A013028

Keyword

nonn

Author

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

Status

approved