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 A362354 #25 Jun 19 2025 00:54:15
%S A362354 1,3,15,108,1029,12288,177147,3000000,58461513,1289945088,31813498119,
%T A362354 867763964928,25949267578125,844424930131968,29713734098717811,
%U A362354 1124440102746243072,45543381089624394897,1966080000000000000000,90125827485245075684223,4372496892684322588065792
%N A362354 a(n) = 3*(n+3)^(n-1).
%C A362354 This gives the third exponential (also called binomial) convolution of {A000272(n+1)} = {A232006(n+1, 1)}, for n >= 0, with e.g.f. (LambertW(-x),(-x)) (LambertW is the principal branch of the Lambert W-function).
%C A362354 This is also the row polynomial P(n, x) of the unsigned triangle A137452, evaluated at x = 3.
%H A362354 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-function</a>
%H A362354 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>
%F A362354 a(n) = Sum_{k=0..n} |A137452(n, k)|*3^k = Sum_{k=0..n} binomial(n-1, k-1)*n^(n-k)*3^k, with the n = 0 term equal to 1 (not 0).
%F A362354 E.g.f.: (LambertW(-x)/(-x))^3.
%F A362354 From _Seiichi Manyama_, Jun 19 2024: (Start)
%F A362354 E.g.f. A(x) satisfies:
%F A362354 (1) A(x) = exp(3*x*A(x)^(1/3)).
%F A362354 (2) A(x) = 1/A(-x*A(x)^(2/3)). (End)
%Y A362354 Column k=3 of A232006 (without leading zeros).
%Y A362354 Cf. A137452.
%K A362354 nonn,easy
%O A362354 0,2
%A A362354 _Wolfdieter Lang_, Apr 24 2023