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A120945 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). 1
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; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..42.

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, Aug 24 2006

EXAMPLE

[1,2], [1,8,18,12], [1,18,108,272,300,120], [1,33,393,2102,5700,8160,5880,1680], ....

CROSSREFS

Row sums give A104209.

Sequence in context: A047688 A089925 A235047 * A235048 A013118 A012961

Adjacent sequences:  A120942 A120943 A120944 * A120946 A120947 A120948

KEYWORD

nonn,tabf

AUTHOR

Vladeta Jovovic, Aug 19 2006

STATUS

approved

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Last modified October 23 07:11 EDT 2019. Contains 328336 sequences. (Running on oeis4.)