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 A370186 #12 Feb 11 2024 09:16:36
%S A370186 1,3,15,90,583,3913,26790,185839,1301575,9183681,65181645,464858661,
%T A370186 3328503814,23913207750,172295708971,1244484142765,9008351053031,
%U A370186 65332552755149,474622993450725,3453219378684621,25158758123093013,183521479226172667,1340195580366321837
%N A370186 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^3)^2 )^n.
%F A370186 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(3*n-k,n-3*k).
%F A370186 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^3)^2) ). See A369484.
%o A370186 (PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A370186 Cf. A370185, A370187.
%Y A370186 Cf. A369484.
%K A370186 nonn
%O A370186 0,2
%A A370186 _Seiichi Manyama_, Feb 11 2024