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 A383233 #13 Apr 20 2025 10:39:38
%S A383233 0,1,11,167,3318,81930,2423208,83582568,3295488816,146241365904,
%T A383233 7214605476480,391735046081664,23216763331632384,1491431668108800768,
%U A383233 103230214859003968512,7659080261784464808960,606407304545822037952512,51033731719180664212641792,4549228202963725560906891264
%N A383233 Expansion of e.g.f. f(x)^3 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
%H A383233 Harvey P. Dale, <a href="/A383233/b383233.txt">Table of n, a(n) for n = 0..355</a>
%F A383233 a(n) = Sum_{k=1..n} k * 3^(k-1) * 5^(n-k) * |Stirling1(n,k)|.
%F A383233 a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-3/5,k)/(n-k).
%F A383233 a(n) = (10*n-9) * a(n-1) - (5*n-7)^2 * a(n-2) for n > 1.
%t A383233 With[{nn=20,f=Surd[1/(1-5x),5]},CoefficientList[Series[f^3 Log[f],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 20 2025 *)
%o A383233 (PARI) a(n) = sum(k=1, n, k*3^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));
%Y A383233 Cf. A383231, A383232, A383234.
%K A383233 nonn
%O A383233 0,3
%A A383233 _Seiichi Manyama_, Apr 20 2025