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 A383051 #13 Apr 15 2025 08:25:38
%S A383051 1,2,5,-1,-116,984,16400,-788418,5474016,941115360,-51647682648,
%T A383051 -264087895512,244846563852864,-16953959408998080,-436871956049596800,
%U A383051 219647419965976413744,-20283048895473275917824,-877465277974899660349440,545297904370739513319183360
%N A383051 a(n) is the n-th term of the inverse Stirling transform of j-> (j+1)^n.
%H A383051 Christian G. Bower, <a href="https://oeis.org/transforms_pari.txt">PARI programs for transforms</a>, 2007.
%H A383051 N. J. A. Sloane, <a href="/transforms.txt">Maple programs for transforms</a>, 2001-2020.
%F A383051 a(n) = Sum_{k=0..n} (k+1)^n * Stirling1(n,k).
%F A383051 a(n) = n! * [x^n] Sum_{k>=0} (k+1)^n * log(1+x)^k / k!.
%F A383051 a(n) = n! * [x^n] (1+x) * Sum_{k=0..n} Stirling2(n+1,k+1) * log(1+x)^k.
%o A383051 (PARI) a(n) = sum(k=0, n, (k+1)^n*stirling(n, k, 1));
%Y A383051 Main diagonal of A383049.
%Y A383051 Cf. A320082, A367820.
%K A383051 sign
%O A383051 0,2
%A A383051 _Seiichi Manyama_, Apr 14 2025