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 A372370 #14 Apr 30 2024 15:47:34
%S A372370 1,1,5,13,53,176,677,2451,9333,34978,133580,508806,1953701,7509178,
%T A372370 28981643,112046213,434289525,1686080622,6557830310,25542229740,
%U A372370 99622788428,389023326600,1520817551742,5951305115982,23310374278437,91380414955176,358506409488102
%N A372370 Coefficient of x^n in the expansion of ( (1+x+x^2)^2 / (1+x) )^n.
%F A372370 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(n-k,n-2*k).
%F A372370 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)^2 ).
%t A372370 a[n_]:=SeriesCoefficient[((1+x+x^2)^2/(1+x))^n,{x,0,n}]; Array[a,27,0] (* _Stefano Spezia_, Apr 30 2024 *)
%o A372370 (PARI) a(n, s=2, t=2, u=-1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A372370 Cf. A027908, A370159, A370160.
%Y A372370 Cf. A002426, A351858, A372382.
%Y A372370 Cf. A166135.
%K A372370 nonn
%O A372370 0,3
%A A372370 _Seiichi Manyama_, Apr 28 2024