A091478 -id:A091478 - cp's OEIS frontend

A091479 Number of graphs with n nodes. Nodes and edges labeled each from their own label set.

1, 1, 2, 16, 1957, 9864101, 3554627472076, 138879579704209680022, 828772446866981044847857913441, 1011182700521015817607065606491025592595137, 325166909258549255903203528672831330994640286650913570126

Offset: 0

Christian G. Bower, Jan 13 2004

nonn

Andrew Howroyd, Table of n, a(n) for n = 0..30

Row sums of A091478.
Cf. A006125.
Cf. A000217, A000522.

a(n)={binomial(n,2)!*sum(k=0, binomial(n,2), 1/k!)} \\ Andrew Howroyd, Feb 12 2020

a(n) = A000522(A000217(n-1)). - Gerald McGarvey, Nov 17 2007

a(0)=1 prepended and terms a(10) and beyond from Andrew Howroyd, Feb 12 2020

A091480 Table of multigraphs (by antidiagonals) with n (>=1) nodes and k (>=0) edges. Each type of object labeled from its own label set.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 9, 6, 1, 0, 1, 27, 36, 10, 1, 0, 1, 81, 216, 100, 15, 1, 0, 1, 243, 1296, 1000, 225, 21, 1, 0, 1, 729, 7776, 10000, 3375, 441, 28, 1, 0, 1, 2187, 46656, 100000, 50625, 9261, 784, 36, 1, 0, 1, 6561, 279936, 1000000, 759375

Offset: 1

Christian G. Bower, Jan 13 2004

			1  0   0    0     0 ...
1  1   1    1     1 ...
1  3   9   27    81 ...
1  6  36  216  1296 ...
1 10 100 1000 10000 ...

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 114 (2.4.44).

Columns 0-8: A000012, A000217(n-1), A000537(n-1), A059827(n-1), A059977(n-1), A059860(n-1), A059978(n-1), A059979(n-1), A059980(n-1).
Rows 1-10: A000007, A000012, A000244, A000400, A011557, A001024, A009965, A009972, A009980, A009989.
Cf. A091478.

a(n, k) = binomial(n, 2)^k.

cp's OEIS Frontend

A091479 Number of graphs with n nodes. Nodes and edges labeled each from their own label set.

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