The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A288789 Number of blocks of size >= 7 in all set partitions of n. 2
 1, 9, 82, 701, 5897, 49854, 427597, 3740609, 33479542, 307119477, 2890138160, 27911144971, 276632735047, 2813333368854, 29349063282197, 313940448544057, 3441759044602385, 38652680805862224, 444450158120668786, 5229815283321976222, 62942722623990478840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 7..575 Wikipedia, Partition of a set FORMULA a(n) = Bell(n+1) - Sum_{j=0..6} binomial(n,j) * Bell(n-j). a(n) = Sum_{j=0..n-7} binomial(n,j) * Bell(j). E.g.f.: (exp(x) - Sum_{k=0..6} x^k/k!) * exp(exp(x) - 1). - Ilya Gutkovskiy, Jun 26 2022 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, 7): seq(a(n), n=7..30); # second Maple program: b:= proc(n) option remember; `if`(n=0, [1, 0], add((p-> p+       `if`(j>6, [0, p[1]], 0))(b(n-j)*binomial(n-1, j-1)), j=1..n))     end: a:= n-> b(n)[2]: seq(a(n), n=7..30);  # Alois P. Heinz, Jun 26 2022 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, 7]; Table[a[n], {n, 7, 30}] (* Jean-François Alcover, May 28 2018, from Maple *) CROSSREFS Column k=7 of A283424. Cf. A000110. Sequence in context: A275917 A293803 A263817 * A033119 A033127 A099371 Adjacent sequences:  A288786 A288787 A288788 * A288790 A288791 A288792 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 15 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)