A377960 -id:A377960 - cp's OEIS frontend

A377958 Expansion of e.g.f. exp(x - x^2)/(1 - x).

1, 2, 3, 4, 17, 126, 787, 5048, 39489, 361882, 3641411, 39948492, 478777873, 6226077014, 87182747667, 1307703873856, 20922694556417, 355686434950578, 6402375749061379, 121645136562423572, 2432901971620591761, 51090940751194252462, 1124000727777806326163

Offset: 0

Seiichi Manyama, Nov 12 2024

nonn

Cf. A293604, A377959, A377960.

Cf. A018191.

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

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

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

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

Original entry on oeis.org

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.

cp's OEIS Frontend

A377958 Expansion of e.g.f. exp(x - x^2)/(1 - x).

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