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A275070 Number of set partitions of [n] such that i-j is a multiple of three for all i,j belonging to the same block. 2
1, 1, 1, 1, 2, 4, 8, 20, 50, 125, 375, 1125, 3375, 11700, 40560, 140608, 548912, 2142868, 8365427, 36140293, 156133187, 674526133, 3184194060, 15031429200, 70957944000, 362451121200, 1851389821260, 9456845543523, 51863510753775, 284431392616875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..699

Wikipedia, Partition of a set

FORMULA

a(n) = Product_{i=0..2} A000110(floor((n+i)/3)).

EXAMPLE

a(7) = 20: 147|25|36, 14|25|36|7, 147|25|3|6, 14|25|3|6|7, 147|2|36|5, 14|2|36|5|7, 147|2|3|5|6, 14|2|3|5|6|7, 17|25|36|4, 1|25|36|47, 1|25|36|4|7, 17|25|3|4|6, 1|25|3|47|6, 1|25|3|4|6|7, 17|2|36|4|5, 1|2|36|47|5, 1|2|36|4|5|7, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.

CROSSREFS

Column k=3 of A275069.

Cf. A000110.

Sequence in context: A225585 A121703 A301467 * A115219 A078160 A218088

Adjacent sequences:  A275067 A275068 A275069 * A275071 A275072 A275073

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 15 2016

STATUS

approved

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Last modified May 15 13:52 EDT 2021. Contains 343920 sequences. (Running on oeis4.)