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 A277391 #17 Feb 16 2025 08:33:36
%S A277391 1,3,34,654,17688,616120,26252496,1322624016,76909665664,
%T A277391 5069558461824,373529452588800,30422117430022912,2713911389090970624,
%U A277391 263171888496899625984,27563036166079327578112,3100736138961250867968000,372888702864658105915244544
%N A277391 a(n) = n!*LaguerreL(n, -2*n).
%H A277391 G. C. Greubel, <a href="/A277391/b277391.txt">Table of n, a(n) for n = 0..250</a>
%H A277391 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H A277391 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%F A277391 a(n) = n! * Sum_{k=0..n} binomial(n, k) * 2^k * n^k / k!.
%F A277391 a(n) ~ (1 + sqrt(3))^(2*n+1) * n^n / (3^(1/4) * 2^(n+1) * exp((2 - sqrt(3))*n)).
%t A277391 Table[n!*LaguerreL[n, -2*n], {n, 0, 20}]
%t A277391 Flatten[{1, Table[n!*Sum[Binomial[n, k]*2^k*n^k/k!, {k, 0, n}], {n, 1, 20}]}]
%o A277391 (PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n,k)*2^k*n^k/k!), ", ")) \\ _G. C. Greubel_, May 15 2018
%o A277391 (Magma) [Factorial(n)*(&+[Binomial(n,k)*2^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, May 15 2018
%Y A277391 Cf. A002720, A087912, A277382.
%Y A277391 Cf. A277373, A277392, A277418, A277419, A277420, A277421, A277422.
%K A277391 nonn
%O A277391 0,2
%A A277391 _Vaclav Kotesovec_, Oct 12 2016