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

0,2

Links

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

Formula

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.

Prog

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

Crossrefs

Cf. A293604, A377958, A377960.

Cf. A377954.

Sequence in context: A027040 A111063 A245116 * A255382 A089475 A351185

Adjacent sequences: A377956 A377957 A377958 * A377960 A377961 A377962

Keyword

nonn

Author

Seiichi Manyama, Nov 12 2024

Status

approved