A321526 - OEIS

%I #27 Nov 14 2018 11:38:00

%S 1,4,40,960,53248,6651904,1839202304,1111322787840,1453210774536192,

%T 4080507553002291200,24448060793158379765760,

%U 310908581955001382242091008,8355018414502495124631718985728,472643828352464917980832865510752256

%N Number of partitioned graphs on n labeled nodes.

%C Bell numbers (partitions of the nodes) multiplied by the number of graphs on the nodes.

%H Peter Baumgartner, <a href="/A321526/b321526.txt">Table of n, a(n) for n = 1..50</a>

%F a(n) = A000110(n) * A006125(n).

%F a(n) = Bell(n) * 2^binomial(n, 2).

%e a(1) = 1 * 1; a(2) = 2 * 2, a(3) = 5 * 8, a(4) = 15 * 64.

%t a[n_] := BellB[n]*2^Binomial[n, 2]; Array[a, 14] (* _Amiram Eldar_, Nov 12 2018 *)

%o (PARI) bell(n)={sum(k=0, n, stirling(n, k, 2))}

%o a(n)=bell(n)*2^binomial(n,2) \\ _Andrew Howroyd_, Nov 12 2018

%Y Cf. A000110, A006125.

%K nonn

%O 1,2

%A _Peter Baumgartner_, Nov 12 2018