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 A288790 Number of blocks of size >= eight in all set partitions of n. 2
 1, 10, 101, 947, 8670, 79249, 730745, 6838642, 65197797, 634656360, 6316333291, 64318009411, 670336612614, 7151290120037, 78085166445577, 872478836270306, 9972817907218608, 116575837400037486, 1393037460835481622, 17010118386233081680, 212160149063581345610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 8..575 Wikipedia, Partition of a set FORMULA a(n) = Bell(n+1) - Sum_{j=0..7} binomial(n,j) * Bell(n-j). a(n) = Sum_{j=0..n-8} 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, 8): seq(a(n), n=8..30); MATHEMATICA Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 8}], {n, 8, 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 - 7)]) print [a(n) for n in range(8, 31)] # Indranil Ghosh, Jul 06 2017 CROSSREFS Column k=8 of A283424. Cf. A000110. Sequence in context: A214390 A293804 A210167 * A280371 A105032 A281102 Adjacent sequences:  A288787 A288788 A288789 * A288791 A288792 A288793 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 15 2017 STATUS approved

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Last modified September 18 22:25 EDT 2020. Contains 337174 sequences. (Running on oeis4.)