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A106238 Triangle read by rows: T(n,m) = number of unlabeled digraphs of order n, n<=9, with m strongly connected components. 1
1, 1, 1, 5, 1, 1, 83, 6, 1, 1, 5048, 88, 6, 1, 1, 1047008, 5146, 89, 6, 1, 1, 705422362, 1052471, 5151, 89, 6, 1, 1, 1580348371788, 706498096, 1052569, 5152, 89, 6, 1, 1, 12139024825260556, 1581059448174, 706503594, 1052574, 5152, 89, 6, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The formula T(n,m) = sum over the partitions of n with m parts 1K1 + 2K2 +  ... + nKn, of Product_{i=1..n}binomial(f(i)+Ki-1, Ki) can be used to count unlabeled graphs of order n with m components if f(i) is the number of non-isomorphic connected components of order i. (In general, f denotes a sequence that counts unlabeled connected combinatorial objects.)

LINKS

Table of n, a(n) for n=1..45.

FORMULA

G.f.: 1/Product_{i>=1}(1-y*x^i)^A035512(i). - Vladeta Jovovic, May 04 2005

Triangle read by rows: T(n, m) = sum over the partitions of n with m parts 1K1 + 2K2 +  ... + nKn, of Product_{i=1..n}binomial(A035512(i)+Ki-1, Ki).

EXAMPLE

T(4,2) = 6 because there are 6 digraphs of order 4 with 2 strongly connected components.

CROSSREFS

Cf. A035512, A057276, A106237, A106239.

Sequence in context: A246051 A111820 A174912 * A173475 A174919 A156952

Adjacent sequences:  A106235 A106236 A106237 * A106239 A106240 A106241

KEYWORD

nonn,tabl

AUTHOR

Washington Bomfim, May 01 2005

STATUS

approved

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Last modified August 6 09:31 EDT 2020. Contains 336245 sequences. (Running on oeis4.)