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A215864 Number of simple labeled graphs on n+4 nodes with exactly n connected components that are trees or cycles. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A221346

Adjacent sequences:  A215861 A215862 A215863 * A215865 A215866 A215867

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Aug 25 2012

STATUS

approved

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Last modified April 7 18:19 EDT 2020. Contains 333306 sequences. (Running on oeis4.)