A109493 a(n) = 7^((n^2 - n)/2).

1, 1, 7, 343, 117649, 282475249, 4747561509943, 558545864083284007, 459986536544739960976801, 2651730845859653471779023381601, 107006904423598033356356300384937784807

Offset: 0

Author

Philippe Deléham, Aug 29 2005

Keywords

• nonn
• easy

Comments

Sequence given by the Hankel transform (see A001906 for definition) of A081178 = {1, 1, 8, 71, 680, 6882, 72528, 788019, ...}; example: det([1, 1, 8, 71; 1, 8, 71, 680; 8, 71, 680, 6882; 71, 680, 6882, 72528]) = 7^6 = 117649.

In general, sequences of the form m^((n^2 - n)/2) enumerate the graphs with n labeled nodes with m types of edge. a(n) therefore is the number of labeled graphs with n nodes with 7 types of edge. - Mark Stander, Apr 11 2019

Crossrefs

Cf. A006125, A047656, A053763, A053764, A109345, A109354.

Programs

PARI

a(n) = 7^binomial(n,2) \\ Charles R Greathouse IV, Jan 17 2012

Formula

a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(7i, j).

G.f. A(x) satisfies: A(x) = 1 + x * A(7*x). - Ilya Gutkovskiy, Jun 04 2020