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 A372410 #11 Apr 30 2024 06:05:26
%S A372410 1,2,12,77,516,3552,24891,176647,1265508,9132530,66288762,483442434,
%T A372410 3539626635,26002266656,191556630375,1414649524077,10469628711396,
%U A372410 77630719516650,576585458828844,4288881479411395,31945446999811266,238233164413294792,1778587750475510316
%N A372410 Coefficient of x^n in the expansion of ( (1-x+x^2) / (1-x)^3 )^n.
%F A372410 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(3*n-k-1,n-2*k).
%F A372410 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^3 / (1-x+x^2) ). See A366049.
%o A372410 (PARI) a(n, s=2, t=1, u=3) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y A372410 Cf. A246437, A262440.
%Y A372410 Cf. A366049.
%K A372410 nonn
%O A372410 0,2
%A A372410 _Seiichi Manyama_, Apr 29 2024