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 A372382 #13 Apr 30 2024 15:48:39
%S A372382 1,1,9,25,169,651,3801,17053,93225,450844,2396859,12043494,63354649,
%T A372382 324888305,1704137493,8839907475,46383701545,242285478474,
%U A372382 1273274074020,6681277302239,35178613785819,185187072845569,976888169385302,5154978257816280,27240094648199961
%N A372382 Coefficient of x^n in the expansion of ( (1+x+x^2)^4 / (1+x)^3 )^n.
%F A372382 a(n) = Sum_{k=0..floor(n/2)} binomial(4*n,k) * binomial(n-k,n-2*k).
%F A372382 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)^4 ). See A372383.
%t A372382 a[n_]:=SeriesCoefficient[((1+x+x^2)^4/(1+x)^3)^n,{x,0,n}]; Array[a,25,0] (* _Stefano Spezia_, Apr 30 2024 *)
%o A372382 (PARI) a(n, s=2, t=4, u=-3) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A372382 Cf. A002426, A351858, A372370.
%Y A372382 Cf. A372383.
%K A372382 nonn
%O A372382 0,3
%A A372382 _Seiichi Manyama_, Apr 29 2024