A377960 Expansion of e.g.f. exp(x - x^2)/(1 - x)^3.

1, 4, 17, 82, 469, 3176, 24829, 219262, 2157257, 23405644, 277601161, 3572553194, 49576701277, 737902011952, 11725479449909, 198112664861206, 3546412902136849, 67047080265355412, 1334894917247980417, 27917550541234128514, 611874855066753173861, 14024463626236493578744

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

a(n) = (n+3)*a(n-1) - 3*(n-1)*a(n-2) + 2*(n-1)*(n-2)*a(n-3) for n > 2.

Prog

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

Crossrefs

Cf. A293604, A377958, A377959.

Cf. A377955.

Sequence in context: A181517 A110771 A082028 * A373931 A052315 A369476

Adjacent sequences: A377957 A377958 A377959 * A377961 A377962 A377963

Keyword

nonn

Author

Seiichi Manyama, Nov 12 2024

Status

approved