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 A370103 #21 Feb 13 2024 10:56:29
%S A370103 1,1,7,28,151,751,3976,20924,112023,602182,3260257,17724928,96766072,
%T A370103 529977917,2910984412,16027963528,88440034711,488918693466,
%U A370103 2707393587802,15014647096172,83380131228401,463593653171495,2580426581343200,14377474236172320
%N A370103 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n+k-1,k) * binomial(4*n-k-1,n-k).
%F A370103 a(n) = [x^n] 1/( (1+x)^2 * (1-x)^3 )^n.
%F A370103 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)^3 ). See A365854.
%F A370103 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(n,n-2*k).
%F A370103 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(2*n-2*k-1,n-2*k).
%o A370103 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k-1, k)*binomial(4*n-k-1, n-k));
%o A370103 (PARI) a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
%o A370103 (PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
%Y A370103 Cf. A351857, A370104.
%Y A370103 Cf. A352373, A370098, A370101.
%Y A370103 Cf. A001700, A348410.
%Y A370103 Cf. A365854.
%K A370103 nonn
%O A370103 0,3
%A A370103 _Seiichi Manyama_, Feb 10 2024