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 A377158 #7 Oct 18 2024 10:49:29
%S A377158 1,7,35,196,994,4578,20118,84540,341397,1335103,5078227,18852428,
%T A377158 68519920,244413820,857393700,2963013816,10102413972,34025396580,
%U A377158 113329367816,373642488044,1220412680410,3951964394642,12695738508950,40484919514284,128216539026261
%N A377158 a(n) = Sum_{k=0..n} binomial(k+6,6) * binomial(k,n-k)^2.
%F A377158 G.f.: (Sum_{k=0..3} A089627(6,k) * (1-x-x^2)^(6-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^(13/2).
%o A377158 (PARI) a(n) = sum(k=0, n, binomial(k+6, 6)*binomial(k, n-k)^2);
%o A377158 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377158 my(N=6, 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 A377158 Cf. A051286, A182884, A377145, A377148, A377152, A377153, A377159.
%Y A377158 Cf. A089627.
%K A377158 nonn
%O A377158 0,2
%A A377158 _Seiichi Manyama_, Oct 18 2024