A352644 Expansion of e.g.f. exp(2 * x * cosh(x)).

1, 2, 4, 14, 64, 282, 1504, 9382, 59392, 417842, 3234304, 25854270, 222423040, 2039652682, 19398688768, 195195414998, 2058666508288, 22509119309922, 257507944431616, 3058883865391726, 37588692110934016, 479523015556635002, 6316374397705781248

Offset: 0

Author

Seiichi Manyama, Mar 25 2022

Keywords

• nonn

Crossrefs

Cf. A003727, A185951, A352645.

Programs

Mathematica

With[{m = 22}, Range[0, m]! * CoefficientList[Series[Exp[2*x*Cosh[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*x*cosh(x))))

PARI

a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));

Formula

a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).

a(n) = Sum_{k=0..n} 2^k * A185951(n,k). - Seiichi Manyama, Feb 18 2025