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 A370172 #12 Feb 11 2024 09:16:23
%S A370172 1,5,51,581,6963,85905,1079943,13756216,176939187,2292988919,
%T A370172 29892396451,391576960230,5150057095527,67962810381653,
%U A370172 899458144305408,11933576896320981,158672857603511987,2113800649819533735,28207266176359605705,376976971371883606824
%N A370172 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^2)^3 )^n.
%F A370172 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(5*n-k,n-2*k).
%F A370172 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^2)^3) ). See A369480.
%o A370172 (PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A370172 Cf. A370170, A370171.
%Y A370172 Cf. A369480.
%K A370172 nonn
%O A370172 0,2
%A A370172 _Seiichi Manyama_, Feb 11 2024