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

0,2

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).

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.

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 *)

Crossrefs

A diagonal of A215861.

Sequence in context: A202083 A330491 A136080 * A190307 A094488 A381709

Adjacent sequences: A215861 A215862 A215863 * A215865 A215866 A215867

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 25 2012

Status

approved