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 A346628 #14 Nov 19 2021 09:19:18
%S A346628 1,0,2,5,22,92,415,1927,9198,44804,221880,1113730,5653747,28975962,
%T A346628 149725355,779178092,4080167790,21483383992,113670233848,604070682354,
%U A346628 3222823434608,17255628041720,92689459311470,499359484166994,2697571066055611,14608820993453132
%N A346628 G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x) * A(x)^3.
%C A346628 Inverse binomial transform of A001764.
%H A346628 Seiichi Manyama, <a href="/A346628/b346628.txt">Table of n, a(n) for n = 0..1000</a>
%F A346628 G.f.: Sum_{k>=0} ( binomial(3*k,k) / (2*k + 1) ) * x^k / (1 + x)^(k+1).
%F A346628 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(3*k,k) / (2*k + 1).
%F A346628 a(n) ~ 23^(n + 3/2) / (81 * sqrt(Pi) * n^(3/2) * 2^(2*n+2)). - _Vaclav Kotesovec_, Jul 30 2021
%F A346628 D-finite with recurrence +2*n*(2*n+1)*a(n) -(15*n-4)*(n-1)*a(n-1) -2*(n-1)*(21*n-22)*a(n-2) -23*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Aug 05 2021
%t A346628 nmax = 25; A[_] = 0; Do[A[x_] = 1/(1 + x) + x (1 + x) A[x]^3 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A346628 nmax = 25; CoefficientList[Series[Sum[(Binomial[3 k, k]/(2 k + 1)) x^k/(1 + x)^(k + 1), {k, 0, nmax}], {x, 0, nmax}], x]
%t A346628 Table[Sum[(-1)^(n - k) Binomial[n, k] Binomial[3 k, k]/(2 k + 1), {k, 0, n}], {n, 0, 25}]
%Y A346628 Cf. A001764, A005043, A188678, A188687, A346627, A346664, A346665, A346666, A346667, A346668.
%K A346628 nonn
%O A346628 0,3
%A A346628 _Ilya Gutkovskiy_, Jul 25 2021