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 A366035 #8 Feb 16 2025 08:34:06
%S A366035 0,1,8,98,1440,23389,404712,7314724,136476912,2608808180,50828498336,
%T A366035 1005682252458,20152470321984,408149824237302,8341496306085040,
%U A366035 171812412714350280,3562961488550366480,74328284438252301996,1558783863783469298016,32844108784368485209320,694957689921176181019520
%N A366035 G.f. A(x) satisfies: A(x) = x * (1 + A(x))^5 / (1 - 3 * A(x)).
%C A366035 Reversion of g.f. for 4-dimensional figurate numbers A002417 (with signs).
%H A366035 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>
%F A366035 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n+k-1,k) * binomial(5*n,n-k-1) * 3^k for n > 0.
%F A366035 a(n) ~ 2^(4*n - 1) * 5^(5*n + 1/2) / (sqrt(Pi) * n^(3/2) * 3^(7*n + 5/2)). - _Vaclav Kotesovec_, Sep 27 2023
%t A366035 nmax = 20; A[_] = 0; Do[A[x_] = x (1 + A[x])^5/(1 - 3 A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A366035 CoefficientList[InverseSeries[Series[x (1 - 3 x)/(1 + x)^5, {x, 0, 20}], x], x]
%t A366035 Join[{0}, Table[1/n Sum[Binomial[n + k - 1, k] Binomial[5 n, n - k - 1] 3^k, {k, 0, n - 1}], {n, 1, 20}]]
%Y A366035 Cf. A002294, A002417, A064087, A365668, A365755, A365816, A366015, A366036, A366037.
%K A366035 nonn
%O A366035 0,3
%A A366035 _Ilya Gutkovskiy_, Sep 26 2023