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 A084943 #39 Aug 28 2025 10:25:53
%S A084943 1,1,10,270,14040,1193400,150368400,26314470000,6104957040000,
%T A084943 1813172240880000,670873729125600000,302564051835645600000,
%U A084943 163384587991248624000000,104075982550425373488000000,77224379052415627128096000000,66026844089815361194522080000000,64442199831659792525853550080000000
%N A084943 Decagorials: n-th polygorial for k=10.
%H A084943 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 A084943 a(n) = polygorial(n, 10) = (A000142(n)/A000079(n))*A084948(n) = (n!/2^n)*Product_{i=0..n-1} (8*i+2) = (n!/2^n)*8^n*Pochhammer(1/4, n) = (n!/2)*4^n*Gamma(n+1/4)*sqrt(2)*Gamma(3/4)/Pi.
%F A084943 a(n) = Product_{k=1..n} k*(4k-3). - _Daniel Suteu_, Nov 01 2017
%F A084943 D-finite with recurrence a(n) -n*(4*n-3)*a(n-1)=0. - _R. J. Mathar_, May 02 2022
%F A084943 a(n) ~ 2^(2*n+1) * n^(2*n + 1/4) * Pi /(Gamma(1/4) * exp(2*n)). - _Amiram Eldar_, Aug 28 2025
%p A084943 a := n->n!/2^n*product(8*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t A084943 polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k -2), n]]; Array[polygorial[10, #] &, 14, 0] (* _Robert G. Wilson v_, Dec 26 2016 *)
%o A084943 (PARI) a(n)=n!/2^n*prod(i=1,n,8*i-6) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A084943 Cf. A006472, A001044, A000680, A068466, A084939, A084940, A084941, A084942, A084944, A085356.
%K A084943 easy,nonn,changed
%O A084943 0,3
%A A084943 Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003