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 A277392 #18 Feb 16 2025 08:33:36
%S A277392 1,4,62,1626,59928,2844120,165100752,11331597942,897635712384,
%T A277392 80602042275756,8090067511468800,897561658361441106,
%U A277392 109072492644378442752,14407931244544181001216,2055559499598438969956352,314997663481165477898736750,51601245736595962597616222208
%N A277392 a(n) = n!*LaguerreL(n, -3*n).
%H A277392 G. C. Greubel, <a href="/A277392/b277392.txt">Table of n, a(n) for n = 0..250</a>
%H A277392 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>
%H A277392 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%F A277392 a(n) = n! * Sum_{k=0..n} binomial(n, k) * 3^k * n^k / k!.
%F A277392 a(n) ~ sqrt(1/2+5/(2*sqrt(21))) * (5+sqrt(21))^n * exp(n*(sqrt(21)-5)/2) * n^n/2^n.
%t A277392 Table[n!*LaguerreL[n, -3*n], {n, 0, 20}]
%t A277392 Flatten[{1, Table[n!*Sum[Binomial[n, k]*3^k*n^k/k!, {k, 0, n}], {n, 1, 20}]}]
%o A277392 (PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n,k)*3^k*n^k/k!), ", ")) \\ _G. C. Greubel_, May 15 2018
%o A277392 (Magma) [Factorial(n)*(&+[Binomial(n,k)*3^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, May 15 2018
%Y A277392 Cf. A002720, A087912, A277382.
%Y A277392 Cf. A277373, A277391, A277418, A277419, A277420, A277421, A277422.
%K A277392 nonn
%O A277392 0,2
%A A277392 _Vaclav Kotesovec_, Oct 12 2016