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 A366037 #9 Feb 16 2025 08:34:06
%S A366037 0,1,10,160,3110,67155,1548526,37346040,930513870,23765376580,
%T A366037 618871054120,16370119905880,438628647940730,11880264846822610,
%U A366037 324739360804852980,8946782070689651280,248184394985913218910,6926162613387923126700,194320992885495965332600,5477763483026946993808960,155070883903415687652796120
%N A366037 G.f. A(x) satisfies: A(x) = x * (1 + A(x))^5 / (1 - 5 * A(x)).
%C A366037 Reversion of g.f. for 4-dimensional figurate numbers A002419 (with signs).
%H A366037 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>
%F A366037 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n+k-1,k) * binomial(5*n,n-k-1) * 5^k for n > 0.
%F A366037 a(n) ~ sqrt((5168 - 869*sqrt(34)) / (17*Pi)) * (22 - sqrt(34))^(5*n) / (2 * n^(3/2) * 3^(3*n + 3/2) * 5^(4*n + 1) * (11*sqrt(34) - 62)^n). - _Vaclav Kotesovec_, Sep 27 2023
%t A366037 nmax = 20; A[_] = 0; Do[A[x_] = x (1 + A[x])^5/(1 - 5 A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A366037 CoefficientList[InverseSeries[Series[x (1 - 5 x)/(1 + x)^5, {x, 0, 20}], x], x]
%t A366037 Join[{0}, Table[1/n Sum[Binomial[n + k - 1, k] Binomial[5 n, n - k - 1] 5^k, {k, 0, n - 1}], {n, 1, 20}]]
%Y A366037 Cf. A002294, A002419, A064089, A365668, A365755, A365818, A366017, A366035, A366036.
%K A366037 nonn
%O A366037 0,3
%A A366037 _Ilya Gutkovskiy_, Sep 26 2023