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 A302171 #14 Mar 02 2024 13:10:56
%S A302171 1,1,4,14,54,213,880,3724,16143,71227,319067,1447160,6633530,30682425,
%T A302171 143028870,671293632,3169572659,15044993968,71752624923,343658572717,
%U A302171 1652266087698,7971518032791,38581202763318,187269381724629,911404238805468,4446493502832481,21742327471261176
%N A302171 G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - x^k*A(x))^k.
%H A302171 Vaclav Kotesovec, <a href="/A302171/b302171.txt">Table of n, a(n) for n = 0..400</a>
%F A302171 a(n) ~ c * d^n / n^(3/2), where d = 5.177446537296361283814259811908762546749... and c = 0.81395777803098291048009263980507199... - _Vaclav Kotesovec_, Sep 27 2023
%F A302171 Radius of convergence r = 0.1931454033945844258723936803941781838... = 1/d and A(r) = 2.2252305561396523944672847657756264073... satisfy (1) A(r) = 1 / Sum_{n>=1} n*r^n/(1 - r^n*A(r)) and (2) A(r) = 1 / Product_{n>=1} (1 - r^n*A(r))^n. - _Paul D. Hanna_, Mar 02 2024
%e A302171 G.f. A(x) = 1 + x + 4*x^2 + 14*x^3 + 54*x^4 + 213*x^5 + 880*x^6 + 3724*x^7 + 16143*x^8 + ...
%e A302171 G.f. A(x) satisfies: A(x) = 1/((1 - x*A(x)) * (1 - x^2*A(x))^2 * (1 - x^3*A(x))^3 * ...).
%t A302171 nmax = 30; A[_] = 0; Do[A[x_] = 1/Product[(1 - x^k*A[x])^k, {k, 1, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, Sep 26 2023 *)
%Y A302171 Cf. A000219, A145267, A145268, A190862, A298260, A298261, A301455, A301624, A301831.
%K A302171 nonn
%O A302171 0,3
%A A302171 _Ilya Gutkovskiy_, Apr 02 2018