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 A362356 #26 Jun 19 2025 01:37:44
%S A362356 1,5,35,320,3645,50000,805255,14929920,313742585,7378945280,
%T A362356 192216796875,5497558138880,171359481538165,5784156907130880,
%U A362356 210264917311285295,8192000000000000000,340611592914758411505,15056807481695325716480,705250197803314844630515
%N A362356 a(n) = 5*(n + 5)^(n-1).
%C A362356 This gives the fifth 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 A362356 This is also the row polynomial P(n, x) of the unsigned triangle A137452, evaluated at x = 5.
%H A362356 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-function</a>
%H A362356 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>
%F A362356 a(n) = Sum_{k=0..n} |A137452(n, k)|*5^k = Sum_{k=0..n} binomial(n-1, k-1)*n^(n-k)*5^k, with the n = 0 term equal to 1 (not 0).
%F A362356 E.g.f.: (LambertW(-x)/(-x))^5.
%F A362356 From _Seiichi Manyama_, Jun 19 2024: (Start)
%F A362356 E.g.f. A(x) satisfies:
%F A362356 (1) A(x) = exp(5*x*A(x)^(1/5)).
%F A362356 (2) A(x) = 1/A(-x*A(x)^(2/5)). (End)
%Y A362356 Column k=5 of A232006 (without leading zeros).
%Y A362356 Cf. A000272, A137452.
%K A362356 nonn,easy
%O A362356 0,2
%A A362356 _Wolfdieter Lang_, Apr 24 2023