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A277423 a(n) = n!*LaguerreL(n, n).

%I A277423 #22 Jul 08 2025 10:40:14
%S A277423 1,0,-2,6,24,-380,720,31794,-361088,-2104056,101548800,-612792290,
%T A277423 -25534891008,593660731404,2831189530624,-361541172525750,
%U A277423 4481749181890560,169464194149739536,-6805365045197340672,-9663483091971306186,6883830206467440640000
%N A277423 a(n) = n!*LaguerreL(n, n).
%H A277423 G. C. Greubel, <a href="/A277423/b277423.txt">Table of n, a(n) for n = 0..415</a>
%H A277423 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H A277423 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%F A277423 a(n) = n! * Sum_{k=0..n} binomial(n, k) * (-1)^k * n^k / k!.
%F A277423 a(n) = n! * [x^n] exp(-n*x/(1 - x))/(1 - x). - _Ilya Gutkovskiy_, Nov 21 2017
%F A277423 a(n) = Sum_{k=0..n} (-n)^(n-k)*k!*binomial(n,k)^2. - _Ridouane Oudra_, Jul 08 2025
%t A277423 Table[n!*LaguerreL[n, n], {n, 0, 20}]
%t A277423 Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]
%t A277423 Table[n! * Hypergeometric1F1[-n, 1, n], {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 20 2020 *)
%o A277423 (PARI) a(n) = n!*sum(k=0,n, binomial(n,k)*(-1)^k*n^k/k!); \\ _G. C. Greubel_, May 16 2018
%o A277423 (Magma) [Factorial(n)*(&+[Binomial(n,k)*(-1)^k*n^k/Factorial(k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, May 16 2018
%Y A277423 Cf. A277373, A277391, A277392, A277418, A277419, A277420, A277421, A277422.
%Y A277423 Cf. A002720, A087912, A277382.
%K A277423 sign
%O A277423 0,3
%A A277423 _Vaclav Kotesovec_, Oct 14 2016