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A125697
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Table, T(n,k) is the number of categories with n morphisms and k objects.
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2
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1, 2, 1, 7, 3, 1, 35, 16, 3, 1, 228, 77, 20, 3, 1, 2237, 485, 111, 21, 3, 1, 31559
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OFFSET
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1,2
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COMMENTS
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This is a two-dimensional Euler transform of A125699.
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LINKS
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Table of n, a(n) for n=1..22.
Eric Weisstein's World of Mathematics, Category
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FORMULA
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G.f. Product_{i=1}^{infinity} Product_{j=1}^{ceiling(i/2)} 1 / (1 - x^i y^j)^A125699(i,j).
T(n,k) = A125701(n-k) when k >= 2/3 n.
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EXAMPLE
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The table starts:
1
2,1
7,3,1
35,16,3,1
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CROSSREFS
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Cf. A125696 (row sums), A058129 (column 1), A125699, A125701, A125726.
Sequence in context: A197328 A136535 A091370 * A090699 A214550 A120903
Adjacent sequences: A125694 A125695 A125696 * A125698 A125699 A125700
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KEYWORD
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tabl,hard,more,nonn
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AUTHOR
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Franklin T. Adams-Watters and Christian G. Bower, Jan 05 2007
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STATUS
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approved
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