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 A125697 Table, T(n,k) is the number of categories with n morphisms and k objects. 2
 1, 2, 1, 7, 3, 1, 35, 16, 3, 1, 228, 77, 20, 3, 1, 2237, 485, 111, 21, 3, 1, 31559 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is a two-dimensional Euler transform of A125699. LINKS Eric Weisstein's World of Mathematics, Category FORMULA G.f.: Product_{i>=1} 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. EXAMPLE The table starts:    1;    2,  1;    7,  3,  1;   35, 16,  3,  1; CROSSREFS Cf. A125696 (row sums), A058129 (column 1), A125699, A125701, A125726. Sequence in context: A136535 A320579 A091370 * A090699 A214550 A120903 Adjacent sequences:  A125694 A125695 A125696 * A125698 A125699 A125700 KEYWORD tabl,hard,more,nonn AUTHOR Franklin T. Adams-Watters and Christian G. Bower, Jan 05 2007 STATUS approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)