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 A084942 #34 Aug 28 2025 10:25:56
%S A084942 1,1,9,216,9936,745200,82717200,12738448800,2598643555200,
%T A084942 678245967907200,220429939569840000,87290256069656640000,
%U A084942 41375581377017247360000,23128949989752641274240000,15056946443328969469530240000,11292709832496727102147680000000,9666559616617198399438414080000000
%N A084942 Enneagorials: n-th polygorial for k=9.
%H A084942 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 A084942 a(n) = polygorial(n, 9) = (A000142(n)/A000079(n))*A084947(n) = (n!/2^n)*Product_{i=0..n-1} (7*i+2) = (n!/2^n)*7^n*Pochhammer(2/7, n) = (n!/2^n)*7^n*Gamma(n+2/7)/Gamma(2/7).
%F A084942 D-finite with recurrence 2*a(n) = n*(7*n-5)*a(n-1). - _R. J. Mathar_, Mar 12 2019
%F A084942 a(n) ~ 7^n * n^(2*n + 2/7) * Pi /(Gamma(2/7) * 2^(n-1) * exp(2*n)). - _Amiram Eldar_, Aug 28 2025
%p A084942 a := n->n!/2^n*product(7*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t A084942 polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k -2), n]]; Array[polygorial[9, #] &, 16, 0] (* _Robert G. Wilson v_, Dec 26 2016 *)
%o A084942 (PARI) a(n)=n!/2^n*prod(i=1,n,7*i-5) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A084942 Cf. A006472, A001044, A000680, A084939, A084940, A084941, A084943, A084944, A085356, A220605.
%K A084942 easy,nonn,changed
%O A084942 0,3
%A A084942 Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003