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 A084940 #41 Aug 28 2025 10:26:11
%S A084940 1,1,7,126,4284,235620,19085220,2137544640,316356606720,
%T A084940 59791398670080,14050978687468800,4018579904616076800,
%U A084940 1374354327378698265600,553864793933615401036800,259762588354865623086259200,140271797711627436466579968000,86407427390362500863413260288000
%N A084940 Heptagorials: n-th polygorial for k=7.
%H A084940 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 A084940 a(n) = polygorial(n, 7) = (A000142(n)/A000079(n))*A047055(n) = (n!/2^n)*Product_{i=0..n-1}(5*i+2) = (n!/2^n)*5^n*Pochhammer(2/5, n) = (n!/2^n)*5^n*Gamma(n+2/5)*sin(2*Pi/5)*Gamma(3/5)/Pi.
%F A084940 D-finite with recurrence 2*a(n) = n*(5*n-3)*a(n-1). - _R. J. Mathar_, Mar 12 2019
%F A084940 a(n) ~ 5^n * n^(2*n + 2/5) * Pi /(Gamma(2/5) * 2^(n-1) * exp(2*n)). - _Amiram Eldar_, Aug 28 2025
%p A084940 a := n->n!/2^n*mul(5*i+2,i=0..n-1); [seq(a(j),j=0..30)];
%t A084940 polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k -2), n]]; Array[ polygorial[7, #] &, 16, 0] (* _Robert G. Wilson v_, Dec 26 2016 *)
%t A084940 Join[{1},FoldList[Times,PolygonalNumber[7,Range[20]]]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 29 2019 *)
%o A084940 (PARI) a(n)=n!/2^n*prod(i=1,n,5*i-3) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A084940 Cf. A006472, A001044, A000680, A084939, A084941, A084942, A084943, A084944, A085356, A246745.
%K A084940 easy,nonn,changed
%O A084940 0,3
%A A084940 Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003