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 A380307 #15 Jan 21 2025 05:00:16
%S A380307 1,1,-3,25,-335,6177,-144947,4128937,-138327615,5327738497,
%T A380307 -231899041475,11255588133945,-602683483719503,35288931375293857,
%U A380307 -2242963870471014963,153791777744471484745,-11314787069889491407103,889087243145447511507969,-74312052321224600661026051
%N A380307 Expansion of e.g.f. exp( (1+5*x)^(1/5) - 1 ).
%H A380307 Seiichi Manyama, <a href="/A380307/b380307.txt">Table of n, a(n) for n = 0..355</a>
%F A380307 a(n) = Sum_{k=0..n} 5^(n-k) * Stirling1(n,k) * Bell(k).
%F A380307 a(n) = (1/e) * 5^n * n! * Sum_{k>=0} binomial(k/5,n)/k!.
%F A380307 a(0) = 1; a(n) = Sum_{k=1..n} (Product_{j=0..k-1} (-5*j+1)) * binomial(n-1,k-1) * a(n-k).
%o A380307 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1+5*x)^(1/5)-1)))
%Y A380307 Cf. A000806, A380208.
%Y A380307 Cf. A000110, A028575.
%K A380307 sign
%O A380307 0,3
%A A380307 _Seiichi Manyama_, Jan 20 2025