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A215774
Number of undirected labeled graphs on n+4 nodes with exactly n cycle graphs as connected components.
2
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
0,2
LINKS
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.
EXAMPLE
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).
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);
CROSSREFS
A diagonal of A215771.
Sequence in context: A124797 A204768 A045508 * A275941 A173359 A199037
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 23 2012
STATUS
approved