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 A380512 #23 Mar 15 2025 09:43:31
%S A380512 1,1,7,91,1753,45001,1447471,56041987,2539200721,131859347473,
%T A380512 7723214721271,503787793244011,36223369111466857,2846582772323685721,
%U A380512 242741539845295265503,22325483241906758894611,2202979676409063904473121,232158319570869255177386017,26024052774273208806612761191
%N A380512 Expansion of e.g.f. exp(x*G(x)^3) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
%H A380512 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%H A380512 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A380512 E.g.f.: exp(G(x)-1), where G(x) is described above.
%F A380512 a(n) = (n-1)! * Sum_{k=0..n-1} binomial(3*n,k)/(n-k-1)! for n > 0.
%F A380512 a(n+1) = n! * LaguerreL(n, 2*n+3, -1).
%F A380512 a(n) = (-1)^(n+1)*U(1-n, 2*(1+n), -1), where U is the Tricomi confluent hypergeometric function. - _Stefano Spezia_, Jan 26 2025
%F A380512 E.g.f.: exp( Series_Reversion( x/(1+x)^3 ) ). - _Seiichi Manyama_, Mar 15 2025
%o A380512 (PARI) a(n) = if(n==0, 1, (n-1)!*pollaguerre(n-1, 2*n+1, -1));
%Y A380512 Cf. A001764, A251569, A380511.
%Y A380512 Cf. A000262, A251568, A380516.
%Y A380512 Cf. A382033.
%K A380512 nonn
%O A380512 0,3
%A A380512 _Seiichi Manyama_, Jan 26 2025