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 A306019 Number of non-isomorphic set-systems of weight n in which all parts have the same size. 11
 1, 1, 2, 2, 4, 2, 10, 2, 17, 14, 33, 2, 167, 2, 186, 491, 785, 2, 5839, 2, 11123, 53454, 15229, 2, 1102924, 53537, 193382, 16334183, 12411062, 2, 382413555, 2, 993814248, 9763321547, 53394774, 1778595972, 402119882757, 2, 1111261718, 9674133468473, 16955983996383 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A set-system of weight n is a finite set of finite nonempty sets whose sizes sum to n. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 FORMULA a(p) = 2 for prime p. - Andrew Howroyd, Aug 29 2019 EXAMPLE Non-isomorphic representatives of the a(6) = 10 set-systems: {{1,2,3,4,5,6}} {{1,2,3},{4,5,6}} {{1,2,5},{3,4,5}} {{1,3,4},{2,3,4}} {{1,2},{1,3},{2,3}} {{1,2},{3,4},{5,6}} {{1,2},{3,5},{4,5}} {{1,3},{2,4},{3,4}} {{1,4},{2,4},{3,4}} {{1},{2},{3},{4},{5},{6}} PROG (PARI) \\ See A283877 for permcount, WeighT, SetTypes. a(n) = {if(n==0, 1, sumdiv(n, d, if(d==1 || d==n, 1, my(s=0); forpart(p=n, s+=permcount(p)*WeighT(SetTypes(p, q->if(d

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Last modified April 20 12:58 EDT 2021. Contains 343135 sequences. (Running on oeis4.)