A381277 Expansion of e.g.f. exp(sinh(3*x) / 3).

1, 1, 1, 10, 37, 172, 1477, 8416, 74377, 683344, 5836969, 67102048, 699721453, 8268521536, 107106298093, 1347611617792, 19462095444241, 279380302430464, 4247519795325649, 68946703997616640, 1122787065355425973, 19697500164381137920, 351304020205694058133

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) = Sum_{k=0..n} 3^(n-k) * A136630(n,k).

Prog

(PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, 3^(n-k)*a136630(n, k));

Crossrefs

Cf. A003724, A009229.

Cf. A136630.

Sequence in context: A199208 A110528 A208674 * A137280 A071261 A373619

Adjacent sequences: A381274 A381275 A381276 * A381278 A381280 A381281

Keyword

nonn

Author

Seiichi Manyama, Feb 18 2025

Status

approved