A330942 - OEIS

A330942

Array read by antidiagonals: A(n,k) is the number of binary matrices with k columns and any number of nonzero rows with n ones in every column and columns in nonincreasing lexicographic order.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 7, 1, 1, 1, 8, 75, 32, 1, 1, 1, 16, 1105, 2712, 161, 1, 1, 1, 32, 20821, 449102, 116681, 842, 1, 1, 1, 64, 478439, 122886128, 231522891, 5366384, 4495, 1, 1, 1, 128, 12977815, 50225389432, 975712562347, 131163390878, 256461703, 24320, 1, 1

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OFFSET

0,8

COMMENTS

The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.

A(n,k) is the number of labeled n-uniform hypergraphs with multiple edges allowed and with k edges and no isolated vertices. When n=2 these objects are multigraphs.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325

FORMULA

A(n,k) = Sum_{j=0..n*k} binomial(binomial(j,n)+k-1, k) * (Sum_{i=j..n*k} (-1)^(i-j)*binomial(i,j)).

A(n, k) = Sum_{j=0..k} abs(Stirling1(k, j))*A262809(n, j)/k!.

A(n, k) = Sum_{j=0..k} binomial(k-1, k-j)*A331277(n, j).

A331638(n) = Sum_{d|n} A(n/d, d).

EXAMPLE

Array begins:

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n\k | 0 1 2 3 4 5

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