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 A372465 #7 May 02 2024 09:46:02
%S A372465 1,4,36,358,3740,40194,439998,4879326,54630316,616194700,6991215286,
%T A372465 79700776588,912207989030,10475536585674,120641989237890,
%U A372465 1392811194744288,16114668707519404,186798818992569818,2168990381036497812,25222834639587149890,293708687012053512870
%N A372465 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^3) )^(2*n).
%F A372465 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+k-1,k) * binomial(5*n-2*k-1,n-3*k).
%F A372465 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^3)^2 ). See A368976.
%o A372465 (PARI) a(n, s=3, t=2, u=2) = 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 A372465 Cf. A368976, A372461.
%K A372465 nonn
%O A372465 0,2
%A A372465 _Seiichi Manyama_, May 01 2024