A352649 Expansion of e.g.f. 1/(1 - 3 * x * cosh(x)).

1, 3, 18, 171, 2160, 34035, 643680, 14203371, 358178688, 10161542691, 320315005440, 11106766229163, 420132741912576, 17216605635562515, 759789379494512640, 35925442734363182955, 1811923104577065615360, 97097117111612660889411, 5509300889675218610552832

Offset: 0

Author

Seiichi Manyama, Mar 25 2022

Keywords

• nonn

Crossrefs

Cf. A205571, A352648.

Cf. A185951.

Programs

Mathematica

With[{m = 17}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*x*Cosh[x]), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*cosh(x))))

PARI

a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));

Formula

a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).

a(n) = Sum_{k=0..n} 3^k * k! * A185951(n,k). - Seiichi Manyama, Jun 25 2025