A318815 Number of triples of set partitions of {1,2,...,n} whose join is {{1,2,...,n}}.

1, 7, 103, 2773, 117697, 7167619, 590978941, 63385879261, 8584707943381, 1434654097736101, 290409845948305321, 70125579500764771585, 19940633217840575968969, 6603748351832744611210549, 2522614472277243822293033719, 1102166886808604068546379343289

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