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A318815 Number of triples of set partitions of {1,2,...,n} whose join is {{1,2,...,n}}. 2
1, 7, 103, 2773, 117697, 7167619, 590978941, 63385879261, 8584707943381, 1434654097736101, 290409845948305321, 70125579500764771585, 19940633217840575968969, 6603748351832744611210549, 2522614472277243822293033719, 1102166886808604068546379343289 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Logarithmic transform of A000110(n)^3.
a(n) = Bell(n)^3 - (1/n) * Sum_{k=1..n-1} binomial(n,k) * Bell(n-k)^3 * k * a(k). - Ilya Gutkovskiy, Jan 17 2020
EXAMPLE
The a(2) = 7 triples:
{{1},{2}} {{1},{2}} {{1,2}}
{{1},{2}} {{1,2}} {{1},{2}}
{{1},{2}} {{1,2}} {{1,2}}
{{1,2}} {{1},{2}} {{1},{2}}
{{1,2}} {{1},{2}} {{1,2}}
{{1,2}} {{1,2}} {{1},{2}}
{{1,2}} {{1,2}} {{1,2}}
MATHEMATICA
nn=10; Table[n!*SeriesCoefficient[Log[1+Sum[BellB[n]^3*x^n/n!, {n, nn}]], {x, 0, n}], {n, nn}]
CROSSREFS
Sequence in context: A177752 A101746 A318398 * A195246 A280644 A322646
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 04 2018
STATUS
approved

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Last modified February 23 08:55 EST 2024. Contains 370272 sequences. (Running on oeis4.)