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 A294352 #10 May 20 2024 11:25:05
%S A294352 1,2,10,160,10400,3390400,6635012800,90899675360000,
%T A294352 9962695319131360000,9827302289744364817600000,
%U A294352 96937502343569678741652977600000,10518214548789290471667075399621491200000,13695360582395151673134516587047571322777664000000
%N A294352 Product of first n terms of the binomial transform of the factorial.
%H A294352 Michael De Vlieger, <a href="/A294352/b294352.txt">Table of n, a(n) for n = 0..43</a>
%H A294352 M. Bahrami-Taghanaki, A. R. Moghaddamfar, Nima Salehy, and Navid Salehy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Moghaddamfar/mogh14.html">Some Identities Involving Stirling Numbers Arising from Matrix Decompositions</a>, J. Int. Seq. (2024) Vol. 24, No. 5, Art. No. 24.5.3. See p. 9.
%F A294352 a(n) ~ c * exp(n+1) * BarnesG(n+2).
%F A294352 a(n) ~ c * n^(n^2/2 + n + 5/12) * (2*Pi)^(n/2 + 1/2) / (A * exp(3*n^2/4 - 13/12))
%F A294352 where c = 0.24314714161123874545254157058990661627416712475691705561000082745...
%F A294352 and A is the Glaisher-Kinkelin constant A074962.
%t A294352 Table[Product[Sum[Binomial[m, k]*k!, {k, 0, m}], {m, 0, n}], {n, 0, 12}]
%Y A294352 Cf. A000522, A047656, A086619, A294353.
%K A294352 nonn
%O A294352 0,2
%A A294352 _Vaclav Kotesovec_, Oct 29 2017