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A063843
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Number of n-multigraphs on 5 nodes.
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| Vladeta Jovovic, Formulae for the number T(n,k) of n-multigraphs on k nodes
Index to sequences with linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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FORMULA
| a(n) = (1/120)*(24*n^2+50*n^3+20*n^4+15*n^6+10*n^7+n^10).
a(n+1) = (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).
G.f. = (1 + 23*x + 473*x^2 + 3681*x^3 + 10717*x^4 + 11221*x^5 + 3779*x^6 + 339*x^7 + 6*x^8)/(1-x)^11 - M. F. Hasler, Jan 19 2012
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MAPLE
| 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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PROG
| (PARI) a(n)=n^2*(n^8+10*n^5+15*n^4+20*n^2+50*n+24)/120 \\ Charles R Greathouse IV, Jan 20 2012
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CROSSREFS
| Cf. A063842. A row of A063841.
Sequence in context: A025190 A160315 A078193 * A192094 A020535 A134500
Adjacent sequences: A063840 A063841 A063842 * A063844 A063845 A063846
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 25 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 02 2001
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