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 A366449 #16 Nov 18 2023 18:27:56
%S A366449 2,5,18,102,970,15947,453872,22174642,1846384884,260939482721,
%T A366449 62454382216334,25285347265901814,17304115945924822724,
%U A366449 20008412370393070905186,39078178288867371807316956,128893469663525965017925474046,717867336460661639426421067202992,6750439274904330523572066561554305664
%N A366449 Number of smooth discrete aggregation functions defined on the finite chain L_n={0,1,...,n-1,n} having neutral element/absorbing element.
%C A366449 The number of smooth discrete aggregation functions on the finite chain L_n={0,1,...,n-1,n} having neutral element/absorbing element e\in L_n, i.e., the number of monotonic increasing binary functions F: L_n^2->L_n such that F(0,0)=0 and F(n,n)=n (discrete aggregation function); F(x+1,y)-F(x,y)<=1 and F(x,y+1)-F(x,y)<= 1 (smooth); and F(x,a)=F(a,x)=x (neutral element) or F(x,a)=F(a,x)=a (absorbing element).
%F A366449 a(n) = 2*Product_{i=0..n-1} (3i+1)!/(n+i)!+ Sum_{a=1..n-1}(Product_{i=0..a-1} (3i+1)!/(a+i)!)*(Product_{i=0..n-a-1} (3i+1)!/(n-a+i)!).
%F A366449 a(n) ~ exp(1/36) * Pi^(1/3) * 3^(3*n^2/2 - 7/36) / (A^(1/3) * Gamma(1/3)^(2/3) * n^(5/36) * 2^(2*n^2 - 17/12)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Nov 18 2023
%t A366449 Table[2*Product[Factorial[3 i + 1]/Factorial[n + i], {i, 0, n - 1}] +
%t A366449 Sum[Product[Factorial[3 i + 1]/Factorial[a + i], {i, 0, a - 1}]*
%t A366449 Product[Factorial[3 i + 1]/Factorial[n - a + i], {i, 0, n - a - 1}], {a, 1, n - 1}], {n, 1, 13}]
%Y A366449 Cf. A005130.
%K A366449 nonn,easy
%O A366449 1,1
%A A366449 _Marc Munar_, Oct 10 2023