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 A344052 #7 May 10 2021 14:43:40
%S A344052 1,-1,-1,8,19,-276,-1002,21216,103395,-2881180,-17620142,609297072,
%T A344052 4483215086,-185182296040,-1592692090420,76512069014400,
%U A344052 753146574607395,-41256108712556460,-457383584443526790,28138583115102810000,346933879489006727610,-23683708768534714984920
%N A344052 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*E1(n, k).
%C A344052 Inverse binomial convolution of the first order Eulerian numbers (A173018).
%F A344052 a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(n - k - j)*(j - k - 1)^n * binomial(n, k)* binomial(n+1, j).
%p A344052 A344052 := n -> add((-1)^(n-k)*binomial(n, k)*combinat:-eulerian1(n, k), k=0..n):
%p A344052 seq(A344052(n), n=0..21);
%t A344052 a[n_] := Sum[Sum[(-1)^(n - k - j)(j - k - 1)^n Binomial[n, k] Binomial[n + 1, j], {j, 0, k}], {k, 0, n}]; Table[a[n], {n, 0, 20}]
%Y A344052 Cf. A173018, A011818 (binomial convolution).
%K A344052 sign
%O A344052 0,4
%A A344052 _Peter Luschny_, May 10 2021