A215774 Number of undirected labeled graphs on n+4 nodes with exactly n cycle graphs as connected components.

0, 12, 127, 742, 3157, 10857, 31899, 82929, 195459, 425139, 864864, 1662661, 3045406, 5349526, 9059946, 14858646, 23684298, 36804558, 55902693, 83180328, 121478203, 174416935, 246559885, 343600335, 472575285, 642108285, 862683822, 1146955887, 1510093452

Offset: 0

Author

Alois P. Heinz, Aug 23 2012

Keywords

• nonn

Examples

			a(1) = 12 = 4!/2: (1-2-3-4-5-1), (1-2-3-5-4-1), (1-2-4-3-5-1), (1-2-4-5-3-1), (1-2-5-3-4-1), (1-2-5-4-3-1), (1-3-2-4-5-1), (1-3-2-5-4-1), (1-3-4-2-5-1), (1-3-5-2-4-1), (1-4-2-3-5-1), (1-4-3-2-5-1).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

A diagonal of A215771.

Programs

Maple

a:= n-> (6864+(20180+(22980+(13295+(4536+(1070+(180+15*n)*
               n)*n)*n)*n)*n)*n)*n/5760:
seq(a(n), n=0..40);

Formula

G.f.: (43*x^3+31*x^2+19*x+12)*x/(1-x)^9.

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(15*n^3+30*n^2+245*n+286)/5760.