OFFSET
1,2
FORMULA
From Vaclav Kotesovec, Apr 16 2018: (Start)
a(n) = 7^(n+1) * Gamma(n) * Gamma(n + 9/7) / (9 * Gamma(2/7) * 2^n).
a(n) ~ Pi * 7^(n+1) * n^(2*n + 2/7) / (9 * Gamma(2/7) * 2^(n-1) * exp(2*n)).
a(n+1) = a(n) * n*(7*n + 9)/2.
(End)
EXAMPLE
The matrix begins:
1 1 1 1 1 1 1 ...
1 9 1 1 1 1 1 ...
1 1 24 1 1 1 1 ...
1 1 1 46 1 1 1 ...
1 1 1 1 75 1 1 ...
1 1 1 1 1 111 1 ...
1 1 1 1 1 1 154 ...
MAPLE
d:=(i, j)->`if`(i<>j, 1, i*(7*i-5)/2):
seq(LinearAlgebra[Determinant](Matrix(n, d)), n=1..16);
MATHEMATICA
nmax = 20; Table[Det[Table[If[i == j, i*(7*i-5)/2, 1], {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Apr 16 2018 *)
RecurrenceTable[{a[n+1] == a[n] * n*(7*n + 9)/2, a[1] == 1}, a, {n, 1, 20}] (* Vaclav Kotesovec, Apr 16 2018 *)
Table[FullSimplify[7^(n + 1) * Gamma[n] * Gamma[n + 9/7] / (9*Gamma[2/7]*2^n)], {n, 1, 15}] (* Vaclav Kotesovec, Apr 16 2018 *)
PROG
(PARI) a(n) = matdet(matrix(n, n, i, j, if (i!=j, 1, i*(7*i-5)/2))); \\ Michel Marcus, Apr 16 2018
CROSSREFS
Cf. A001106 (nonagonal numbers).
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Apr 15 2018
STATUS
approved