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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

Table of n, a(n) for n=1..22.

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.)