A007833 Number of point-labeled reduced two-graphs with n nodes.

1, 0, 1, 1, 28, 448, 18788, 1419852, 207249896, 58206408344, 31725488477648, 33830818147141904, 71068681534173472576, 295648155633330113713344, 2444510010072634827916776064, 40269686339597630128483872278656, 1323732128140903183968664175047409152

Offset: 1

Author

Peter J. Cameron

Keywords

• nonn

Comments

Also number of (n-1)-node labeled mating graphs without isolated nodes, cf. A006024. - Vladeta Jovovic, Mar 23 2004

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..83
• P. J. Cameron, Counting two-graphs related to trees, Elec. J. Combin., Vol. 2, #R4.

Crossrefs

Cf. A092430 (connected).

Programs

Mathematica

Array[Sum[StirlingS1[#, k] 2^((k - 1) (k - 2)/2), {k, #}] &, 15] (* Michael De Vlieger, Feb 03 2018 *)

Formula

a(n) = Sum_{k=1..n} s(n, k) * 2^((k-1) * (k-2) / 2) where s(n, k) are the Stirling numbers of the first kind. - Sean A. Irvine, Feb 03 2018