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A052296 Triangle read by rows: T(n,k) = number of labeled digraphs with n nodes and k arcs and without directed paths of length >=2, with 0 <= k <= floor(n^2/4). 4
1, 1, 1, 2, 1, 6, 6, 1, 12, 36, 32, 6, 1, 20, 120, 280, 280, 120, 20, 1, 30, 300, 1320, 2910, 3492, 2400, 960, 210, 20, 1, 42, 630, 4480, 17220, 39144, 56294, 53760, 35070, 15680, 4662, 840, 70, 1, 56, 1176, 12320, 73220, 269136, 654304, 1108928, 1362900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..50.

FORMULA

G.f. for n-th row: Sum_{k=0..n} binomial(n, k)*((1+x)^k-1)^(n-k). - Vladeta Jovovic, Apr 04 2003

E.g.f.: Sum(exp(y*((1+x)^n-1))*y^n/n!, n = 0 .. infinity). - Vladeta Jovovic, May 28 2004

EXAMPLE

[1],[1],[1,2],[1,6,6],[1,12,36,32,6],[1,20,120,280,280,120,20]

CROSSREFS

Cf. A001831.

Sequence in context: A063007 A202190 A089231 * A019538 A269646 A269336

Adjacent sequences:  A052293 A052294 A052295 * A052297 A052298 A052299

KEYWORD

nonn,tabf

AUTHOR

Vladeta Jovovic, Feb 08 2000

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)