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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 Alois P. Heinz, Table of n, a(n) for n = 1..233 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 Cf. A000110, A000258, A001247, A008277, A048994, A059849, A060639, A181939, A318389, A318391, A318393, A318398, A318399. Sequence in context: A177752 A101746 A318398 * A195246 A280644 A322646 Adjacent sequences: A318812 A318813 A318814 * A318816 A318817 A318818 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.)