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 A302911 #25 Apr 18 2018 03:30:53
%S A302911 1,6,102,3366,181764,14541120,1614064320,237267455040,44606281547520,
%T A302911 10437869882119680,2974792916404108800,1014404384493801100800,
%U A302911 407790562566508042521600,190845983281125763900108800,102865984988526786742158643200
%N A302911 Determinant of n X n matrix whose main diagonal consists of the first n 7-gonal numbers and all other elements are 1's.
%F A302911 From _Vaclav Kotesovec_, Apr 16 2018: (Start)
%F A302911 a(n) = 5^(n + 1) * Gamma(n) * Gamma(n + 7/5) / (7 * Gamma(2/5) * 2^n).
%F A302911 a(n) ~ Pi * 5^(n+1) * n^(2*n + 2/5) / (7 * Gamma(2/5) * 2^(n-1) * exp(2*n)).
%F A302911 a(n+1) = a(n) * n*(5*n + 7)/2.
%F A302911 (End)
%e A302911 The matrix begins:
%e A302911 1 1 1 1 1 1 1 ...
%e A302911 1 7 1 1 1 1 1 ...
%e A302911 1 1 18 1 1 1 1 ...
%e A302911 1 1 1 34 1 1 1 ...
%e A302911 1 1 1 1 55 1 1 ...
%e A302911 1 1 1 1 1 81 1 ...
%e A302911 1 1 1 1 1 1 112 ...
%p A302911 d:=(i,j)->`if`(i<>j,1,i*(5*i-3)/2):
%p A302911 seq(LinearAlgebra[Determinant](Matrix(n,d)),n=1..20);
%t A302911 nmax = 20; Table[Det[Table[If[i == j, i*(5*i - 3)/2, 1], {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* _Vaclav Kotesovec_, Apr 16 2018 *)
%t A302911 Table[FullSimplify[5^(n + 1) * Gamma[n] * Gamma[n + 7/5] / (7 * Gamma[2/5] * 2^n)], {n, 1, 15}] (* _Vaclav Kotesovec_, Apr 16 2018 *)
%o A302911 (PARI) a(n) = matdet(matrix(n, n, i, j, if (i!=j, 1, i*(5*i-3)/2))); \\ _Michel Marcus_, Apr 16 2018
%Y A302911 Cf. A000566 (heptagonal numbers).
%Y A302911 Cf. Determinant of n X n matrix whose main diagonal consists of the first n k-gonal numbers and all other elements are 1's: A000142 (k=2), A067550 (k=3), A010791 (k=4, with offset 1), A302909 (k=5), A302910 (k=6), this sequence (k=7), A302912 (k=8), A302913 (k=9), A302914 (k=10).
%K A302911 nonn
%O A302911 1,2
%A A302911 _Muniru A Asiru_, Apr 15 2018