A289216 a(n) = n! * Laguerre(n,-10).

1, 11, 142, 2086, 34184, 616120, 12083920, 255749840, 5801633920, 140276126080, 3598075308800, 97512721964800, 2782552712473600, 83347512973644800, 2613606571616819200, 85594543750221568000, 2921314815145299968000, 103704333851191177216000

Offset: 0

Author

Alois P. Heinz, Jun 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..429
• Eric Weisstein's World of Mathematics, Laguerre Polynomial
• Wikipedia, Laguerre polynomials
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Column k=10 of A289192.

Cf. A160587, A160589.

Programs

Magma

m:=25; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(10*x/(1-x))/(1-x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018

Maple

a:= n-> n! * add(binomial(n, i)*10^i/i!, i=0..n):
seq(a(n), n=0..20);

Mathematica

Table[n!*LaguerreL[n, -10], {n, 0, 20}] (* Indranil Ghosh, Jul 04 2017 *)

PARI

my(x = 'x + O('x^30)); Vec(serlaplace(exp(10*x/(1-x))/(1-x))) \\ Michel Marcus, Jul 04 2017

PARI

a(n) = n!*pollaguerre(n, 0, -10); \\ Michel Marcus, Feb 05 2021

Python

from mpmath import *
mp.dps=100
def a(n): return int(fac(n)*laguerre(n, 0, -10))
print([a(n) for n in range(21)]) # Indranil Ghosh, Jul 04 2017

Formula

E.g.f.: exp(10*x/(1-x))/(1-x).

a(n) = n! * Sum_{i=0..n} 10^i/i! * binomial(n,i).

a(n) = n! * A160587(n)/A160589(n).

a(n) ~ exp(-5 + 2*sqrt(10*n) - n) * n^(n + 1/4) / (2^(3/4)*5^(1/4)) * (1 + 643/(48*sqrt(10*n))). - Vaclav Kotesovec, Nov 13 2017

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * Sum_{n>=0} 10^n * x^n / (n!)^2. - Ilya Gutkovskiy, Jul 17 2020