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 A377159 #9 Oct 18 2024 10:49:24
%S A377159 1,8,44,264,1446,7152,33516,149688,640233,2642992,10582220,41249000,
%T A377159 157050660,585621960,2143442400,7715164176,27353809188,95660348904,
%U A377159 330377130644,1127996393656,3810881349814,12750188169312,42276102419916,139008143200536,453526927536969
%N A377159 a(n) = Sum_{k=0..n} binomial(k+7,7) * binomial(k,n-k)^2.
%F A377159 G.f.: (Sum_{k=0..3} A089627(7,k) * (1-x-x^2)^(7-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^(15/2).
%o A377159 (PARI) a(n) = sum(k=0, n, binomial(k+7, 7)*binomial(k, n-k)^2);
%o A377159 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377159 my(N=7, M=30, x='x+O('x^M), X=1-x-x^2, Y=3); 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 A377159 Cf. A051286, A182884, A377145, A377148, A377152, A377153, A377158.
%Y A377159 Cf. A089627.
%K A377159 nonn
%O A377159 0,2
%A A377159 _Seiichi Manyama_, Oct 18 2024