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 A370269 #8 Feb 14 2024 10:48:50
%S A370269 1,1,9,37,233,1251,7461,43219,257769,1534096,9224259,55607850,
%T A370269 336885029,2046705428,12472585155,76185639162,466380345065,
%U A370269 2860318763352,17571932737128,108111252582449,666049600308483,4108363051479346,25369393216077370
%N A370269 Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^2)^3 )^n.
%F A370269 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(2*n-2*k-1,n-2*k).
%F A370269 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^2)^3 ). See A365878.
%o A370269 (PARI) a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
%Y A370269 Cf. A348410, A370103.
%Y A370269 Cf. A365878.
%K A370269 nonn
%O A370269 0,3
%A A370269 _Seiichi Manyama_, Feb 13 2024