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%I #18 Sep 08 2022 08:46:20
%S 1,2,32,1422,124832,18246850,4005713952,1232956594814,506672220394496,
%T 267992015325604578,177340024595660672000,143531889358151618790862,
%U 139482579412432078779322368,160267575964062522718064075618,214924620455826226723051817295872
%N a(n) = n! * Laguerre(n, n*(n-1), -n).
%H G. C. Greubel, <a href="/A295418/b295418.txt">Table of n, a(n) for n = 0..213</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F a(n) = n! * Sum_{k=0..n} binomial(n^2,n-k)*n^k/k!.
%F a(n) ~ exp(1/2) * n^(2*n).
%F a(n) = n! * [x^n] exp(n*x/(1 - x))/(1 - x)^(n^2-n+1). - _Ilya Gutkovskiy_, Nov 23 2017
%t Table[n!*LaguerreL[n,n*(n-1),-n],{n,0,15}]
%t Join[{1},Table[n!*Sum[Binomial[n^2,n-k]*n^k/k!,{k,0,n}],{n,1,15}]]
%o (PARI) for(n=0,25, print1(n!*sum(k=0,n, binomial(n^2, n-k)*n^k/k!), ", ")) \\ _G. C. Greubel_, May 13 2018
%o (PARI) a(n) = n!*pollaguerre(n, n*(n-1), -n); \\ _Michel Marcus_, Feb 05 2021
%o (Magma) [Factorial(n)*(&+[Binomial(n^2, n-k)*n^k/Factorial(k): k in [0..n]]): n in [0..25]]; // _G. C. Greubel_, May 13 2018
%Y Cf. A277373, A295385, A295406, A295407, A295408, A295409.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 22 2017
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