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A152059 a(n) is the number of ways 2n-1 seats can be occupied by at most n people for n>=1, with a(0)=1. 3
1, 2, 13, 136, 1961, 36046, 805597, 21204548, 642451441, 22021483546, 842527453421, 35591363004352, 1645373927307673, 82625931422081126, 4478815087922020861, 260648364396903639676, 16208855884741850686817 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..366

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

FORMULA

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

Central terms of triangle A086885 (after initial term).

a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^n. - Ilya Gutkovskiy, Oct 02 2017

a(n) ~ 2^(2*n - 1/2) * n^n / exp(n-1). - Vaclav Kotesovec, Oct 02 2017

a(n) = n! * pollaguerre(n, n-1, -1). - Seiichi Manyama, May 01 2021

MATHEMATICA

Table[(-1)^n * HypergeometricU[-n, n, -1], {n, 0, 20}] (* Vaclav Kotesovec, Oct 02 2017 *)

PROG

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

(PARI) a(n) = n!*pollaguerre(n, n-1, -1); \\ Seiichi Manyama, May 01 2021

CROSSREFS

Cf. A082545, A086885, A343832.

Sequence in context: A246875 A242004 A187021 * A132063 A318003 A143137

Adjacent sequences:  A152056 A152057 A152058 * A152060 A152061 A152062

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 22 2008

STATUS

approved

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Last modified June 14 19:28 EDT 2021. Contains 345038 sequences. (Running on oeis4.)