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 A279662 #9 Feb 16 2025 08:33:38
%S A279662 1,1,7,154,7700,731500,117771500,29678418000,11040371496000,
%T A279662 5796195035400000,4144279450311000000,3920488359994206000000,
%U A279662 4790836775912919732000000,7411424492337286825404000000,14266992147749277138902700000000,33670101468688294047810372000000000
%N A279662 a(n) = (2/3)^n*Gamma(n+3/4)*Gamma(n+1)*Gamma(n+2)/Gamma(3/4).
%C A279662 Hexagonal pyramidal factorial numbers.
%C A279662 More generally, the m-gonal pyramidal factorial numbers is 6^(-n)*(m-2)^n*Gamma(n+1)*Gamma(n+2)*Gamma(n+3/(m-2))/Gamma(3/(m-2)), m>2.
%H A279662 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalPyramidalNumber.html">Hexagonal Pyramidal Number</a>
%H A279662 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H A279662 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A279662 a(n) = Product_{k=1..n} k*(k + 1)*(4*k - 1)/6, a(0)=1.
%F A279662 a(n) = Product_{k=1..n} A002412(k), a(0)=1.
%F A279662 a(n) ~ (2*Pi)^(3/2)*(2/3)^n*n^(3*n+9/4)/(Gamma(3/4)*exp(3*n)).
%t A279662 FullSimplify[Table[(2/3)^n Gamma[n + 3/4] Gamma[n + 1] Gamma[n + 2]/Gamma[3/4], {n, 0, 15}]]
%o A279662 (Magma) [Round((2/3)^n*Gamma(n+3/4)*Gamma(n+1)*Gamma(n+2) / Gamma(3/4)): n in [0..20]]; // _Vincenzo Librandi_, Dec 17 2016
%Y A279662 Cf. A002412.
%Y A279662 Cf. A000680 (hexagonal factorial numbers).
%Y A279662 Cf. A087047 (tetrahedral factorial numbers), A135438 (square pyramidal factorial numbers), A167484 (pentagonal pyramidal factorial numbers), A279663 (heptagonal pyramidal factorial numbers).
%K A279662 nonn
%O A279662 0,3
%A A279662 _Ilya Gutkovskiy_, Dec 16 2016