A109354 - OEIS

%I #38 Jun 05 2020 09:57:47

%S 1,1,6,216,46656,60466176,470184984576,21936950640377856,

%T 6140942214464815497216,10314424798490535546171949056,

%U 103945637534048876111514866313854976,6285195213566005335561053533150026217291776,2280250319867037997421842330085227917956272625811456

%N a(n) = 6^((n^2 - n)/2).

%C 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.

%C 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

%H Andrew Howroyd, <a href="/A109354/b109354.txt">Table of n, a(n) for n = 0..50</a>

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

%F G.f. A(x) satisfies: A(x) = 1 + x * A(6*x). - _Ilya Gutkovskiy_, Jun 04 2020

%t Table[6^((n^2-n)/2),{n,0,10}] (* _Harvey P. Dale_, May 28 2013 *)

%o (PARI) a(n) = 6^((n^2 - n)/2); \\ _Michel Marcus_, Apr 12 2019

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

%K nonn

%O 0,3

%A _Philippe Deléham_, Aug 25 2005

%E Terms a(11) and beyond from _Andrew Howroyd_, Jan 02 2020