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 A084944 #39 Aug 28 2025 10:25:49
%S A084944 1,1,11,330,19140,1818300,256380300,50250538800,13065140088000,
%T A084944 4350691649304000,1805537034461160000,913601739437346960000,
%U A084944 553642654099032257760000,395854497680808064298400000,329746796568113117560567200000,316556924705388592858144512000000,346946389477105897772526385152000000
%N A084944 Hendecagorials: n-th polygorial for k=11.
%H A084944 G. C. Greubel, <a href="/A084944/b084944.txt">Table of n, a(n) for n = 0..220</a>
%H A084944 Daniel Dockery, <a href="https://web.archive.org/web/20140617132401/http://danieldockery.com/res/math/polygorials.pdf">Polygorials, Special "Factorials" of Polygonal Numbers</a>, preprint, 2003.
%F A084944 a(n) = polygorial(n, 11) = (A000142(n)/A000079(n))*A084949(n) = (n!/2^n)*Product_{i=0..n-1} (9*i+2) = (n!/2^n)*9^n*Pochhammer(2/9, n) = (n!/2^n)*9^n*Gamma(n+2/9)/Gamma(2/9).
%F A084944 D-finite with recurrence 2*a(n) = n*(9*n-7)*a(n-1). - _R. J. Mathar_, Mar 12 2019
%F A084944 a(n) ~ 9^n * n^(2*n + 2/9) * Pi /(Gamma(2/9) * 2^(n-1) * exp(2*n)). - _Amiram Eldar_, Aug 28 2025
%p A084944 a := n->n!/2^n*product(9*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t A084944 polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k - 2), n]]; Array[polygorial[11, #] &, 16, 0] (* _Robert G. Wilson v_, Dec 13 2016 *)
%Y A084944 Cf. A006472, A001044, A000680, A084939, A084940, A084941, A084942, A084943, A085356.
%K A084944 easy,nonn,changed
%O A084944 0,3
%A A084944 Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003