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 A372369 #9 Apr 29 2024 09:28:38
%S A372369 1,2,12,65,388,2352,14565,91289,577764,3683459,23621462,152203482,
%T A372369 984598741,6390596591,41596873869,271424778015,1774892605284,
%U A372369 11628321367815,76311803660025,501554760288813,3300889231760238,21750690436059188,143481522241226962
%N A372369 Coefficient of x^n in the expansion of ( (1+x+x^2)^3 / (1+x) )^n.
%F A372369 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(2*n-k,n-2*k).
%F A372369 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^2)^3 ).
%o A372369 (PARI) a(n, s=2, t=3, u=-1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A372369 Cf. A351858, A370170, A370171, A370172.
%Y A372369 Cf. A347953.
%K A372369 nonn
%O A372369 0,2
%A A372369 _Seiichi Manyama_, Apr 28 2024