A109354 a(n) = 6^((n^2 - n)/2).

1, 1, 6, 216, 46656, 60466176, 470184984576, 21936950640377856, 6140942214464815497216, 10314424798490535546171949056, 103945637534048876111514866313854976, 6285195213566005335561053533150026217291776, 2280250319867037997421842330085227917956272625811456

Offset: 0

Author

Philippe Deléham, Aug 25 2005

Keywords

• nonn

Comments

Sequence given by the Hankel transform (see A001906 for definition) of A078018 = {1, 1, 7, 55, 469, 4237, 39907, 387739, ...}; example: det([1, 1, 7, 55; 1, 7, 55, 469; 7, 55, 469, 4237; 55, 469, 4237, 39907]) = 6^6 = 46656.

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 6 types of edge. - Mark Stander, Apr 11 2019

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000400, A006125, A047656, A053763, A053764, A109345.

Programs

Mathematica

Table[6^((n^2-n)/2),{n,0,10}] (* Harvey P. Dale, May 28 2013 *)

PARI

a(n) = 6^((n^2 - n)/2); \\ Michel Marcus, Apr 12 2019

Formula

a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(6i, j).

G.f. A(x) satisfies: A(x) = 1 + x * A(6*x). - Ilya Gutkovskiy, Jun 04 2020

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 02 2020