A380044 E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x)*A(x) ).

1, 1, 7, 81, 1393, 32025, 924831, 32208337, 1314511297, 61553580849, 3253663709335, 191661481308561, 12451241630689137, 884434637282286025, 68195094329460133231, 5672843158404577658385, 506413381554227338302721, 48290505275596520116029537, 4899034372132659112326787239

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

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

Crossrefs

Cf. A295238, A380045.

Sequence in context: A379856 A371027 A058575 * A355220 A375475 A285062

Adjacent sequences: A380041 A380042 A380043 * A380045 A380046 A380047

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2025

Status

approved