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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<serprec(q, x), x^d*polcoef(q, d))))[n]); s/n!)))} \\ Andrew Howroyd, Sep 01 2019

CROSSREFS

Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306020, A306021.

Sequence in context: A053204 A152061 A103314 * A194560 A111741 A111793

Adjacent sequences:  A306016 A306017 A306018 * A306020 A306021 A306022

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 17 2018

EXTENSIONS

Terms a(12) and beyond from Andrew Howroyd, Sep 01 2019

STATUS

approved

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