A381412 E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) / A(x) ).

1, 2, 4, 10, 64, 754, 9024, 109050, 1544960, 27480162, 567449600, 12641553258, 303021248512, 7982668175954, 231306526932992, 7245659221444186, 242226980924424192, 8623216994933650114, 327015684198600278016, 13169904418920596839626, 560434137147666884198400

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381411.

a(n) = 2 * Sum_{k=0..n} (2*n-2*k+2)^(k-1) * 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) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*a136630(n, k));

Crossrefs

Cf. A136630, A381411.

Sequence in context: A368588 A326325 A080090 * A125263 A326949 A215439

Adjacent sequences: A381409 A381410 A381411 * A381413 A381414 A381415

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2025

Status

approved