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A289212 a(n) = n! * Laguerre(n,-6). 4
1, 7, 62, 654, 7944, 108696, 1649232, 27422352, 495057024, 9631281024, 200682406656, 4455296877312, 104921038236672, 2610989435003904, 68430995893131264, 1883330926998829056, 54286270223002140672, 1635031821385383247872, 51347572582353094508544 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..434

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

FORMULA

E.g.f.: exp(6*x/(1-x))/(1-x).

a(n) = n! * Sum_{i=0..n} 6^i/i! * binomial(n,i).

a(n) = n! * A160607(n)/A160608(n).

a(n) ~ exp(-3 + 2*sqrt(6*n) - n) * n^(n + 1/4) / (2^(3/4)*3^(1/4)) * (1 + 97/(16*sqrt(6*n))). - Vaclav Kotesovec, Nov 13 2017

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * Sum_{n>=0} 6^n * x^n / (n!)^2. - Ilya Gutkovskiy, Jul 17 2020

MAPLE

a:= n-> n! * add(binomial(n, i)*6^i/i!, i=0..n):

seq(a(n), n=0..20);

MATHEMATICA

Table[n!*LaguerreL[n, -6], {n, 0, 20}] (* Indranil Ghosh, Jul 04 2017 *)

PROG

(Python)

from mpmath import *

mp.dps=100

def a(n): return int(fac(n)*laguerre(n, 0, -6))

print [a(n) for n in range(21)] # Indranil Ghosh, Jul 04 2017

(PARI) x = 'x + O('x^30); Vec(serlaplace(exp(6*x/(1-x))/(1-x))) \\ Michel Marcus, Jul 04 2017

CROSSREFS

Column k=6 of A289192.

Cf. A160607, A160608.

Sequence in context: A024089 A327588 A287481 * A060005 A055066 A216534

Adjacent sequences:  A289209 A289210 A289211 * A289213 A289214 A289215

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 28 2017

STATUS

approved

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Last modified September 30 17:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)