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 A377186 #15 May 11 2025 09:26:02
%S A377186 1,0,6,6,30,60,170,420,1050,2660,6552,16380,40362,99792,245520,603372,
%T A377186 1480050,3624192,8863712,21647340,52811616,128700000,313341756,
%U A377186 762206016,1852565650,4499346072,10919990460,26485897932,64201490352,155536089240,376606931436
%N A377186 Expansion of 1/(1 - 4*x^2 - 4*x^3)^(3/2).
%H A377186 Vincenzo Librandi, <a href="/A377186/b377186.txt">Table of n, a(n) for n = 0..1500</a>
%F A377186 a(0) = 1, a(1) = 0, a(2) = 6; a(n) = (4*(n+1)*a(n-2) + 2*(2*n+3)*a(n-3))/n.
%F A377186 a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(2*k,k) * binomial(k,n-2*k).
%t A377186 Table[Sum[(2*k+1)*Binomial[2*k,k]*Binomial[k,n-2*k],{k,0,Floor[n/2]}],{n,0,30}] (* _Vincenzo Librandi_, May 11 2025 *)
%o A377186 (PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(2*k, k)*binomial(k, n-2*k));
%o A377186 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/(1 - 4*x^2 - 4*x^3)^(3/2))); // _Vincenzo Librandi_, May 11 2025
%Y A377186 Cf. A115962, A377189, A377190.
%Y A377186 Cf. A374497.
%K A377186 nonn
%O A377186 0,3
%A A377186 _Seiichi Manyama_, Oct 19 2024