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.
%I A295418 #19 Feb 16 2025 08:33:52
%S A295418 1,2,32,1422,124832,18246850,4005713952,1232956594814,506672220394496,
%T A295418 267992015325604578,177340024595660672000,143531889358151618790862,
%U A295418 139482579412432078779322368,160267575964062522718064075618,214924620455826226723051817295872
%N A295418 a(n) = n! * Laguerre(n, n*(n-1), -n).
%H A295418 G. C. Greubel, <a href="/A295418/b295418.txt">Table of n, a(n) for n = 0..213</a>
%H A295418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H A295418 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%H A295418 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A295418 a(n) = n! * Sum_{k=0..n} binomial(n^2,n-k)*n^k/k!.
%F A295418 a(n) ~ exp(1/2) * n^(2*n).
%F A295418 a(n) = n! * [x^n] exp(n*x/(1 - x))/(1 - x)^(n^2-n+1). - _Ilya Gutkovskiy_, Nov 23 2017
%t A295418 Table[n!*LaguerreL[n,n*(n-1),-n],{n,0,15}]
%t A295418 Join[{1},Table[n!*Sum[Binomial[n^2,n-k]*n^k/k!,{k,0,n}],{n,1,15}]]
%o A295418 (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 A295418 (PARI) a(n) = n!*pollaguerre(n, n*(n-1), -n); \\ _Michel Marcus_, Feb 05 2021
%o A295418 (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 A295418 Cf. A277373, A295385, A295406, A295407, A295408, A295409.
%K A295418 nonn
%O A295418 0,2
%A A295418 _Vaclav Kotesovec_, Nov 22 2017