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 A377153 #12 Oct 18 2024 10:49:20
%S A377153 1,6,27,140,651,2772,11354,44640,169371,624742,2248575,7922124,
%T A377153 27397937,93214632,312559200,1034507696,3384194616,10954244952,
%U A377153 35118346760,111602517096,351819819414,1100912299156,3421515852834,10566654790176,32441857824859,99060134392422
%N A377153 a(n) = Sum_{k=0..n} binomial(k+5,5) * binomial(k,n-k)^2.
%F A377153 G.f.: (Sum_{k=0..2} A089627(5,k) * (1-x-x^2)^(5-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^(11/2).
%o A377153 (PARI) a(n) = sum(k=0, n, binomial(k+5, 5)*binomial(k, n-k)^2);
%o A377153 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377153 my(N=5, 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 A377153 Cf. A051286, A182884, A377145, A377148, A377152, A377158, A377159.
%Y A377153 Cf. A001874, A089627.
%K A377153 nonn
%O A377153 0,2
%A A377153 _Seiichi Manyama_, Oct 18 2024