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 A288786 Number of blocks of size >= four in all set partitions of n. 2
 1, 6, 37, 225, 1395, 8944, 59585, 413117, 2981310, 22380814, 174600298, 1413841252, 11868587577, 103155618776, 927141821215, 8606806236367, 82430269073469, 813600584094320, 8267450613029789, 86406853732930699, 927993270700444588, 10232636504064477996 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..575 Wikipedia, Partition of a set FORMULA a(n) = Bell(n+1) - Sum_{j=0..3} binomial(n,j) * Bell(n-j). a(n) = Sum_{j=0..n-4} binomial(n,j) * Bell(j). MAPLE b:= proc(n) option remember; `if`(n=0, 1, add(       b(n-j)*binomial(n-1, j-1), j=1..n))     end: g:= proc(n, k) option remember; `if`(n g(n, 4): seq(a(n), n=4..30); MATHEMATICA b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Binomial[n-1, j-1], {j, 1, n}]]; g[n_, k_] := g[n, k] = If[n < k, 0, g[n, k+1] + Binomial[n, k]*b[n - k]]; a[n_] := g[n, 4]; Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 28 2018, from Maple *) CROSSREFS Column k=4 of A283424. Cf. A000110. Sequence in context: A244618 A033116 A033124 * A180032 A022035 A255119 Adjacent sequences:  A288783 A288784 A288785 * A288787 A288788 A288789 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 15 2017 STATUS approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)