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 A383053 #10 Apr 15 2025 08:26:34
%S A383053 1,16,97,515,2744,15177,88033,536882,3441439,23151411,163135410,
%T A383053 1201594675,9232595661,73858810120,614045917741,5296398334735,
%U A383053 47321198203496,437310785441381,4174403973827181,41107555809612466,417122543915965091,4356601173778017487
%N A383053 a(n) = Sum_{k=0..n} (k+1)^4 * Stirling2(n,k).
%C A383053 Stirling transform of (n+1)^4.
%H A383053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StirlingTransform.html">Stirling Transform</a>
%F A383053 a(n) = A362925(n+4,4).
%F A383053 E.g.f.: Sum_{k>=0} (k+1)^4 * (exp(x) - 1)^k / k!.
%F A383053 E.g.f.: exp(exp(x) - 1) * Sum_{k=0..4} Stirling2(5,k+1) * (exp(x) - 1)^k.
%o A383053 (PARI) a(n) = sum(k=0, n, (k+1)^4*stirling(n, k, 2));
%o A383053 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^4*(exp(x)-1)^k/k!)))
%Y A383053 Cf. A000110, A222748, A362925.
%K A383053 nonn
%O A383053 0,2
%A A383053 _Seiichi Manyama_, Apr 14 2025