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 A372463 #7 May 02 2024 09:46:06
%S A372463 1,3,21,159,1261,10268,85065,713345,6036381,51438741,440780736,
%T A372463 3794261496,32784723361,284184613586,2470101750095,21520640950334,
%U A372463 187885215032925,1643315666085399,14396340879235851,126302446713155886,1109524512806397656
%N A372463 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^3)^2 )^n.
%F A372463 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+k-1,k) * binomial(4*n-2*k-1,n-3*k).
%F A372463 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 A368974.
%o A372463 (PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, (-1)^k*binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
%Y A372463 Cf. A368974, A372459.
%K A372463 nonn
%O A372463 0,2
%A A372463 _Seiichi Manyama_, May 01 2024