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 A377149 #10 Oct 18 2024 10:48:58
%S A377149 1,0,4,4,10,40,30,180,215,580,1316,1960,5719,8624,20420,39536,71985,
%T A377149 160584,276664,588180,1099786,2098480,4201594,7665724,15266640,
%U A377149 28422684,54252560,103928876,193166861,371012360,690296162,1304353740,2450895828,4565652908
%N A377149 a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,3) * binomial(k,n-2*k)^2.
%F A377149 G.f.: (1-x^2-x^3) * ((1-x^2-x^3)^2 + 6*x^5) / ((1-x^2-x^3)^2 - 4*x^5)^(7/2).
%o A377149 (PARI) a(n) = sum(k=0, n\2, binomial(k+3, 3)*binomial(k, n-2*k)^2);
%o A377149 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377149 my(N=3, M=40, x='x+O('x^M), X=1-x^2-x^3, Y=5); Vec(sum(k=0, N\2, a089627(N, k)*X^(N-2*k)*x^(Y*k))/(X^2-4*x^Y)^(N+1/2))
%Y A377149 Cf. A377148, A377150.
%Y A377149 Cf. A089627.
%K A377149 nonn
%O A377149 0,3
%A A377149 _Seiichi Manyama_, Oct 18 2024