A330260 a(n) = n! * Sum_{k=0..n} binomial(n,k) * n^(n - k) / k!.

1, 2, 17, 352, 13505, 830126, 74717857, 9263893892, 1513712421377, 315230799073690, 81499084718806001, 25612081645835777192, 9615370149488574778177, 4250194195208050117007942, 2184834047906975645398282625, 1292386053018890618812398220876

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..232

Formula

a(n) = n! * [x^n] exp(x/(1 - n*x)) / (1 - n*x).

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

a(n) ~ sqrt(2*Pi) * BesselI(0,2) * n^(2*n + 1/2) / exp(n). - Vaclav Kotesovec, Dec 18 2019

Mathematica

Join[{1}, Table[n! Sum[Binomial[n, k] n^(n - k)/k!, {k, 0, n}], {n, 1, 15}]]
Join[{1}, Table[n^n n! LaguerreL[n, -1/n], {n, 1, 15}]]
Table[n! SeriesCoefficient[Exp[x/(1 - n x)]/(1 - n x), {x, 0, n}], {n, 0, 15}]

Prog

(PARI) a(n) = n! * sum(k=0, n, binomial(n, k) * n^(n-k)/k!); \\ Michel Marcus, Dec 18 2019
(Magma) [Factorial(n)*&+[Binomial(n, k)*n^(n-k)/Factorial(k):k in [0..n]]:n in [0..15]]; // Marius A. Burtea, Dec 18 2019

Crossrefs

Cf. A002720, A025167, A061711, A102757, A102773, A187021, A277373, A277452, A293146, A330497.

Main diagonal of A341014.

Sequence in context: A307315 A378044 A373324 * A243509 A128159 A319591

Adjacent sequences: A330257 A330258 A330259 * A330261 A330262 A330263

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 18 2019

Status

approved