A368449 Expansion of e.g.f. exp(x) / (1 + log(1 - 2*x)/2).

1, 2, 7, 42, 365, 4090, 55699, 890722, 16341849, 338128594, 7786397471, 197460558394, 5467207989957, 164085022299146, 5305738076252587, 183876885720455218, 6798985094507177137, 267160159254659407650, 11116956337133269707319, 488348854052875260086474

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 2^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A291979, A368450.

Cf. A227917.

Sequence in context: A366453 A345368 A353257 * A317349 A158840 A359717

Adjacent sequences: A368446 A368447 A368448 * A368450 A368451 A368452

Keyword

nonn

Author

Seiichi Manyama, Dec 24 2023

Status

approved