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A070070
Rounded value of n*L_n(-1) where L is the Laguerre polynomial.
1
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
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
KEYWORD
nonn
AUTHOR
Karol A. Penson, Apr 19 2002
STATUS
approved