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Search: id:A063843
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| A063843 |
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Number of n-multigraphs on 5 nodes. |
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+0
9
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| 0, 1, 34, 792, 10688, 90005, 533358, 2437848, 9156288, 29522961, 84293770, 217993600, 519341472, 1154658869, 2420188694, 4821091920, 9187076352, 16837177281, 29809183410, 51172613512, 85448030080, 139159855989
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equivalently, number of ways to color edges of complete graph on 5 nodes with n colors, under action of symmetric group S_5, of order 120, with cycle index on edges given by (1/120)*(24*x5^2 + 30*x2*x4^2 + 20*x3^3*x1 + 20*x3*x6*x1 + 15*x1^2*x2^4 + 10*x1^4*x2^3 + x1^10). Setting all x_i = n gives the sequence.
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LINKS
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Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes
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FORMULA
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a(n) = (1/120)*(24*n^2+50*n^3+20*n^4+15*n^6+10*n^7+n^10).
a(n) = (1/5!)*(n^10 + 10*n^9 + 45*n^8 + 130*n^7 + 295*n^6 + 552*n^5 + 805*n^4 + 900*n^3 + 774*n^2 + 448*n + 120) (with a different offset).
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MAPLE
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f:=n-> 1/120*(24*n^2+50*n^3+20*n^4+15*n^6+10*n^7+n^10);
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CROSSREFS
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Cf. A063842. A row of A063841.
Sequence in context: A025190 A160315 A078193 this_sequence A020535 A134500 A098607
Adjacent sequences: A063840 A063841 A063842 this_sequence A063844 A063845 A063846
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Aug 25 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 02 2001
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