A377958 -id:A377958 - cp's OEIS frontend

A377959 Expansion of e.g.f. exp(x - x^2)/(1 - x)^2.

1, 3, 9, 31, 141, 831, 5773, 45459, 403161, 3990331, 43544721, 518940423, 6706062949, 93404895351, 1394851282581, 22230473112571, 376610264357553, 6758060929028979, 128047472471583001, 2554547113522500591, 53523844242070603581, 1175091669834676927663

Offset: 0

Seiichi Manyama, Nov 12 2024

nonn

Cf. A293604, A377958, A377960.

Cf. A377954.

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

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

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

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Nov 12 2024

nonn

Cf. A293604, A377958, A377959.

Cf. A377955.

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

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.

cp's OEIS Frontend

A377959 Expansion of e.g.f. exp(x - x^2)/(1 - x)^2.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula