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 A288791 Number of blocks of size >= nine in all set partitions of n. 2
 1, 11, 122, 1245, 12325, 121136, 1195147, 11915997, 120572790, 1241499241, 13030331671, 139549798524, 1525923634907, 17041290249637, 194394900237176, 2264977282222371, 26951265841776186, 327445918493429897, 4060993235341162405, 51396034231430455550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 9,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 9..575 Wikipedia, Partition of a set FORMULA a(n) = Bell(n+1) - Sum_{j=0..8} binomial(n,j) * Bell(n-j). a(n) = Sum_{j=0..n-9} binomial(n,j) * Bell(j). E.g.f.: (exp(x) - Sum_{k=0..8} 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, 9): seq(a(n), n=9..30); MATHEMATICA Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 9}], {n, 9, 30}] (* Indranil Ghosh, Jul 06 2017 *) PROG (Python) from sympy import bell, binomial def a(n): return sum([binomial(n, j)*bell(j) for j in range(n - 8)]) print([a(n) for n in range(9, 31)]) # Indranil Ghosh, Jul 06 2017 CROSSREFS Column k=9 of A283424. Cf. A000110. Sequence in context: A176595 A067218 A293805 * A049666 A163462 A334000 Adjacent sequences:  A288788 A288789 A288790 * A288792 A288793 A288794 KEYWORD nonn,changed AUTHOR Alois P. Heinz, Jun 15 2017 STATUS approved

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Last modified July 5 18:33 EDT 2022. Contains 355101 sequences. (Running on oeis4.)