cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A332679 a(n) = (-1)^n * n! * Laguerre(n, 4*n).

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%I A332679 #18 Feb 05 2021 07:50:34
%S A332679 1,3,34,642,16920,571880,23577552,1147008912,64304389504,
%T A332679 4081584090240,289302692908800,22648001532831488,1940655970832219136,
%U A332679 180654087647513945088,18153823412468554639360,1958590905998560664832000,225799980396482832660529152,27702168947661388727726931968
%N A332679 a(n) = (-1)^n * n! * Laguerre(n, 4*n).
%H A332679 Vaclav Kotesovec, <a href="/A332679/b332679.txt">Table of n, a(n) for n = 0..335</a>
%F A332679 A302112(n) = (a(n) - 2*n*A332680(n)) * binomial(2*n, n) / 2^n.
%F A332679 a(n) / (n*A332680(n)) ~ 2.
%F A332679 a(n) ~ c * n^(n + 1/6) * exp(n), where c = Gamma(1/3) / (2^(5/6) * 3^(1/6) * sqrt(Pi)) = 0.706332637459...
%t A332679 Table[(-1)^n*n!*LaguerreL[n, 4*n], {n, 0, 20}]
%t A332679 Join[{1}, Table[n! * Sum[(-1)^(n-k) * Binomial[n, k] * (4*n)^k/k!, {k, 0, n}], {n, 1, 20}]]
%t A332679 Table[(-1)^n*n!*Hypergeometric1F1[-n, 1, 4*n], {n, 0, 20}]
%o A332679 (PARI) a(n) = (-1)^n*n!*pollaguerre(n, 0, 4*n); \\ _Michel Marcus_, Feb 05 2021
%Y A332679 Cf. A277423, A332692, A332693, A332694, A332695.
%Y A332679 Cf. A277418, A295408, A302112, A332680.
%K A332679 nonn
%O A332679 0,2
%A A332679 _Vaclav Kotesovec_, Feb 19 2020