A381281 Expansion of e.g.f. 1/(1 - x * cosh(3*x)).

1, 1, 2, 33, 240, 2145, 33120, 480753, 7878528, 158696577, 3384322560, 78934776129, 2053186983936, 57231998680545, 1714372871178240, 55323775198258065, 1899762412262031360, 69264871449203672577, 2677542944055160209408, 109197154520146527569505

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• nonn

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A205571, A381280.

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*3^(n-k)*a185951(n, k));

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 9^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).

a(n) = Sum_{k=0..n} k! * 3^(n-k) * A185951(n,k).