A070070 Rounded value of n*L_n(-1) where L is the Laguerre polynomial.

0, 2, 7, 17, 35, 64, 111, 182, 286, 436, 647, 938, 1336, 1871, 2583, 3520, 4741, 6320, 8347, 10930, 14199, 18312, 23460, 29869, 37808, 47600, 59624, 74331, 92250, 114006, 140329, 172077, 210249, 256010, 310717, 375943, 453513, 545538, 654453

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Eric Weisstein's World of Mathematics, Laguerre Polynomial.

Formula

a(n) ~ exp(2*sqrt(n) - 1/2) * n^(3/4) / (2*sqrt(Pi)) * (1 + 31/(48*sqrt(n))). - Vaclav Kotesovec, Nov 14 2017

a(n) = round(n * [x^n] exp(x/(1 - x))/(1 - x)). - Ilya Gutkovskiy, Jun 05 2018

a(n) = round(n * Sum_{k=0..n} binomial(n, k) / k!). - Sean A. Irvine, Jun 01 2024

Maple

a := n->round(expand(n*LaguerreL(n, -1)));

Mathematica

a[n_] := Round[n*LaguerreL[n, 0, -1]]

Prog

(PARI) {a(n) = if( n<0, 0, round(n * polcoeff(exp(x/(1-x) + x*O(x^n)) / (1-x), n)))}; /* Michael Somos, Dec 04 2002 */
(PARI) for(n=0, 40, print1(round(n*sum(k=0, n, binomial(n, k)/k!)), ", ")) \\ G. C. Greubel, May 14 2018
(Magma) [Round(n*(&+[Binomial(n, k)/Factorial(k): k in [0..n]])): n in [0..40]]; // G. C. Greubel, May 14 2018

Crossrefs

Sequence in context: A145066 A014148 A367185 * A318054 A033937 A116576

Adjacent sequences: A070067 A070068 A070069 * A070071 A070072 A070073

Keyword

nonn

Author

Karol A. Penson, Apr 19 2002

Status

approved