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 A375259 #15 Aug 08 2024 08:30:32
%S A375259 1,6,42,224,1134,5292,23562,100584,415701,1671670,6570564,25325664,
%T A375259 95982068,358442280,1321336152,4815108288,17367199983,62063418186,
%U A375259 219942717918,773542367136,2701767769470,9376778431020,32353614992790,111032853586200,379152389532735
%N A375259 Expansion of (1 - 3*x + 6*x^2 - 4*x^3)/(1 - 2*x - 3*x^2)^(9/2).
%H A375259 Seiichi Manyama, <a href="/A375259/b375259.txt">Table of n, a(n) for n = 0..1000</a>
%F A375259 a(n) = (binomial(n+5,4)/5) * Sum_{k=0..floor(n/2)} binomial(n+1,n-2*k) * binomial(2*k+1,k).
%F A375259 a(n) = (binomial(n+5,4)/5) * A005717(n+1).
%F A375259 a(n) = ((n+5)/(n*(n+2))) * ((2*n+1)*a(n-1) + 3*(n+4)*a(n-2)).
%o A375259 (PARI) my(N=30, x='x+O('x^N)); Vec((1-3*x+6*x^2-4*x^3)/(1-2*x-3*x^2)^(9/2))
%Y A375259 Column k=5 of A091869 (with a different offset).
%Y A375259 Cf. A005717, A375260.
%K A375259 nonn
%O A375259 0,2
%A A375259 _Seiichi Manyama_, Aug 08 2024