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 A277418 #16 Feb 16 2025 08:33:36
%S A277418 1,5,98,3246,151064,9052120,663449040,57490690544,5749754436992,
%T A277418 651830574374784,82599621627948800,11569798584488362240,
%U A277418 1775052172071446510592,296026752508667034942464,53320241823337034415908864,10315767337287172256717568000
%N A277418 a(n) = n!*LaguerreL(n, -4*n).
%H A277418 G. C. Greubel, <a href="/A277418/b277418.txt">Table of n, a(n) for n = 0..250</a>
%H A277418 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H A277418 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%F A277418 a(n) = n! * Sum_{k=0..n} binomial(n, k) * 4^k * n^k / k!.
%F A277418 a(n) ~ sqrt(2 + 3/sqrt(2)) * (3 + 2*sqrt(2))^n * exp((-3 + 2*sqrt(2))*n) * n^n / 2.
%t A277418 Table[n!*LaguerreL[n, -4*n], {n, 0, 20}]
%t A277418 Flatten[{1, Table[n!*Sum[Binomial[n, k] * 4^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]
%o A277418 (PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n,k)*4^k*n^k/k!), ", ")) \\ _G. C. Greubel_, May 15 2018
%o A277418 (Magma) [Factorial(n)*(&+[Binomial(n,k)*4^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, May 15 2018
%Y A277418 Cf. A277373, A277391, A277392, A277419, A277420, A277421, A277422.
%Y A277418 Cf. A002720, A087912, A277382, A332679.
%K A277418 nonn
%O A277418 0,2
%A A277418 _Vaclav Kotesovec_, Oct 14 2016