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A320438 Irregular triangle read by rows where T(n,d) is the number of set partitions of {1,...n} with all block-sums equal to d, where d is a divisor of 1 + ... + n. 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 7, 1, 1, 9, 1, 1, 1, 1, 43, 35, 1, 1, 102, 62, 1, 1, 1, 1, 68, 595, 1, 1, 17, 187, 871, 1480, 361, 1, 1, 2650, 657, 1, 1, 9294, 1, 1, 23728, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

Triangle begins:

    1

    1

    1    1

    1    1

    1    1

    1    1

    1    4    1

    1    3    7    1

    1    9    1

    1    1

    1   43   35    1

    1  102   62    1

    1    1

    1   68  595    1

    1   17  187  871 1480  361    1

    1 2650  657    1

Row 8 counts the following set partitions:

  {{18}{27}{36}{45}}  {{1236}{48}{57}}  {{12348}{567}}  {{12345678}}

                      {{138}{246}{57}}  {{12357}{468}}

                      {{156}{237}{48}}  {{12456}{378}}

                                        {{1278}{3456}}

                                        {{1368}{2457}}

                                        {{1458}{2367}}

                                        {{1467}{2358}}

MATHEMATICA

spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];

Table[Length[spsu[Select[Subsets[Range[n]], Total[#]==d&], Range[n]]], {n, 12}, {d, Select[Divisors[n*(n+1)/2], #>=n&]}]

CROSSREFS

Row lengths are A164978. Row sums are A035470.

Cf. A000110, A000258, A008277, A112956, A164977, A275714, A279375, A300335, A320423, A320424, A321455, A321469.

Sequence in context: A261790 A174834 A100642 * A255511 A014518 A316584

Adjacent sequences:  A320435 A320436 A320437 * A320439 A320440 A320441

KEYWORD

nonn,tabf,more

AUTHOR

Gus Wiseman, Jan 08 2019

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)