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 A306019 Number of non-isomorphic set-systems of weight n in which all parts have the same size. 10
 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 October 17 01:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)