A357663 Expansion of e.g.f. cosh( (exp(4*x) - 1)/2 ).

1, 0, 4, 48, 464, 4480, 48448, 621824, 9320704, 154890240, 2746131456, 51237908480, 1007228375040, 20965557829632, 463091379159040, 10826828061147136, 266438312153120768, 6861616219559034880, 184128217520198123520, 5135753969867535941632

Offset: 0

Author

Seiichi Manyama, Oct 07 2022

Keywords

• nonn

Crossrefs

Cf. A024430, A357661, A357662.

Cf. A065143, A357650, A357666.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Cosh[(Exp[4x]-1)/2],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 13 2025 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(cosh((exp(4*x)-1)/2)))

PARI

a(n) = sum(k=0, n\2, 4^(n-k)*stirling(n, 2*k, 2));

Formula

a(n) = Sum_{k=0..floor(n/2)} 4^(n-k) * Stirling2(n,2*k).