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A052296
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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).
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4
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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; internal format)
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OFFSET
| 0,4
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FORMULA
| G.f. for n-th row: Sum_{k=0..n} binomial(n, k)*((1+x)^k-1)^(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 04 2003
E.g.f.: Sum(exp(y*((1+x)^n-1))*y^n/n!, n = 0 .. infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 28 2004
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EXAMPLE
| [1],[1],[1,2],[1,6,6],[1,12,36,32,6],[1,20,120,280,280,120,20]
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CROSSREFS
| Cf. A001831.
Sequence in context: A063007 A202190 A089231 * A019538 A046521 A104684
Adjacent sequences: A052293 A052294 A052295 * A052297 A052298 A052299
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KEYWORD
| nonn,tabf
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 08 2000
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