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 A364474 #17 Apr 18 2025 13:20:26
%S A364474 1,1,4,16,77,403,2228,12800,75653,457022,2809266,17514200,110480475,
%T A364474 703850686,4522217364,29268545416,190645760149,1248817411471,
%U A364474 8221323983431,54365667330636,360954069730636,2405225494066647,16080210766344354,107828663888705292
%N A364474 G.f. satisfies A(x) = 1 + x*A(x)^3 + x^2*A(x).
%H A364474 Michael De Vlieger, <a href="/A364474/b364474.txt">Table of n, a(n) for n = 0..1175</a>
%H A364474 Paul Barry, <a href="https://arxiv.org/abs/2504.09719">Notes on Riordan arrays and lattice paths</a>, arXiv:2504.09719 [math.CO], 2025. See p. 26.
%F A364474 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k,k) * binomial(3*n-6*k,n-2*k) / (2*n-4*k+1).
%F A364474 D-finite with recurrence 2*n*(2*n+1)*(3*n-7)*a(n) -3*(3*n-1)*(3*n-7)*(3*n-2) *a(n-1) -2*(n-3)*(18*n^2-33*n+4) *a(n-2) +2*(18*n^3-141*n^2+287*n-64) *a(n-4) -2*(n-4)*(3*n-1)*(2*n-13)*a(n-6)=0. - _R. J. Mathar_, Jul 27 2023
%p A364474 A364474 := proc(n)
%p A364474 add( binomial(3*n-5*k,k) * binomial(3*n-6*k,n-2*k)/(2*n-4*k+1),k=0..n/2) ;
%p A364474 end proc:
%p A364474 seq(A364474(n),n=0..80); # _R. J. Mathar_, Jul 27 2023
%t A364474 Table[Sum[Binomial[3*n - 5*k, k]*Binomial[3*n - 6*k, n - 2*k]/(2*n - 4*k + 1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* _Wesley Ivan Hurt_, May 25 2024 *)
%o A364474 (PARI) a(n) = sum(k=0, n\2, binomial(3*n-5*k, k)*binomial(3*n-6*k, n-2*k)/(2*n-4*k+1));
%Y A364474 Cf. A002293, A104979, A186997, A255673, A361245, A364475, A364478.
%K A364474 nonn
%O A364474 0,3
%A A364474 _Seiichi Manyama_, Jul 26 2023