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 A383052 #11 Apr 15 2025 08:26:39
%S A383052 1,8,35,153,706,3479,18313,102678,610989,3844525,25492752,177579961,
%T A383052 1295811637,9879799744,78525094847,649253421173,5573667453498,
%U A383052 49595062947091,456689512735421,4345710521536150,42675672248378721,431963852263306569,4501627598926298992
%N A383052 a(n) = Sum_{k=0..n} (k+1)^3 * Stirling2(n,k).
%C A383052 Stirling transform of (n+1)^3.
%H A383052 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F A383052 a(n) = A362925(n+3,3).
%F A383052 E.g.f.: Sum_{k>=0} (k+1)^3 * (exp(x) - 1)^k / k!.
%F A383052 E.g.f.: exp(exp(x) - 1) * Sum_{k=0..3} Stirling2(4,k+1) * (exp(x) - 1)^k.
%o A383052 (PARI) a(n) = sum(k=0, n, (k+1)^3*stirling(n, k, 2));
%o A383052 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^3*(exp(x)-1)^k/k!)))
%Y A383052 Cf. A000110, A222636, A362925.
%K A383052 nonn
%O A383052 0,2
%A A383052 _Seiichi Manyama_, Apr 14 2025