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A120945
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Triangle T(n,k) of number of labeled directed multigraphs (with loops), without isolated vertices, with n arrows and k vertices (n = 1,2,.., k = 1..2*n).
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1
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1, 2, 1, 8, 18, 12, 1, 18, 108, 272, 300, 120, 1, 33, 393, 2102, 5700, 8160, 5880, 1680, 1, 54, 1122, 10688, 53550, 153132, 258720, 255360, 136080, 30240, 1, 82, 2754, 42752, 351650, 1688892, 5025832, 9540272, 11566800, 8668800, 3659040, 665280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| T(n,k) = Sum_{j=0..k} (-1)^(k-j)*binomial(k,j)*binomial(j^2+n-1,n). Row sums give A104209.
E.g.f.: exp(-x)*Sum((1-y)^(-n^2)*x^n/n!,n=0..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 24 2006
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EXAMPLE
| [1,2], [1,8,18,12], [1,18,108,272,300,120], [1,33,393,2102,5700,8160,5880,1680], ....
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CROSSREFS
| Row sums give A104209.
Sequence in context: A199928 A047688 A089925 * A013118 A012961 A013124
Adjacent sequences: A120942 A120943 A120944 * A120946 A120947 A120948
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KEYWORD
| nonn,tabf
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2006
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