A215864 Number of simple labeled graphs on n+4 nodes with exactly n connected components that are trees or cycles.

0, 137, 1267, 6412, 23597, 70707, 183099, 424809, 904299, 1795794, 3367364, 6017011, 10318126, 17075786, 27395466, 42765846, 65157498, 97139343, 142014873, 203980238, 288306403, 401547685, 551779085, 748864935, 1004761485, 1333856160, 1753346322, 2283660477

Offset: 0

Author

Alois P. Heinz, Aug 25 2012

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

A diagonal of A215861.

Programs

Maple

a:= n-> binomial(n+4,5)*(3886+(2285+(390+15*n)*n)*n)/48:
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[(7x^3+59x^2-34x-137)x/(x-1)^9,{x,0,30}],x] (* Harvey P. Dale, Jul 18 2019 *)

Formula

G.f.: (7*x^3+59*x^2-34*x-137)*x/(x-1)^9.

a(n) = C(n+4,5)*(15*n^3+390*n^2+2285*n+3886)/48.