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Search: id:A060514
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| A060514 |
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Triangle T(n,k) of series-reduced (or homeomorphically irreducible) labeled graphs with n nodes and k edges, k=0..binomial(n,2). |
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+0
2
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| 1, 1, 1, 1, 1, 3, 0, 0, 1, 6, 3, 4, 0, 0, 1, 1, 10, 15, 20, 5, 0, 5, 20, 15, 10, 1, 1, 15, 45, 75, 90, 96, 135, 315, 510, 760, 843, 765, 395, 105, 15, 1, 1, 21, 105, 245, 525, 777, 1302, 3045, 7455, 16275, 30135, 50190, 70805, 81690, 70605, 43239, 18774, 5880, 1330
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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FORMULA
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E.g.f. : (1+x*y)^(-1/2)*exp(x*y/2-x^2*y^2/4)*Sum_{k=0..inf}((1+x)*exp(-x^2*y/(1+x*y)))^binomial(k, 2)*(exp(1/2*x^3*y^2/(1+x*y)))^k*x^k/k!
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EXAMPLE
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[1], [1], [1, 1], [1, 3, 0, 0], [1, 6, 3, 4, 0, 0, 1], [1, 10, 15, 20, 5, 0, 5, 20, 15, 10, 1], [1, 15, 45, 75, 90, 96, 135, 315, 510, 760, 843, 765, 395, 105, 15, 1], [1, 21, 105, 245, 525, 777, 1302, 3045, 7455, 16275, 30135, 50190, 70805, 81690, 70605, 43239, 18774, 5880, 1330, 210, 21, 1], ...
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CROSSREFS
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Row sums: A003514.
Sequence in context: A090030 A080159 A144299 this_sequence A096936 A115979 A067168
Adjacent sequences: A060511 A060512 A060513 this_sequence A060515 A060516 A060517
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 23 2001
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