The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A288786

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A288786

Number of blocks of size >= four in all set partitions of n.
(history; published version)

#16 by Joerg Arndt at Sun Jun 26 05:52:15 EDT 2022

STATUS

reviewed

approved

#15 by Vaclav Kotesovec at Sun Jun 26 04:24:56 EDT 2022

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proposed

reviewed

#14 by Ilya Gutkovskiy at Sat Jun 25 03:54:05 EDT 2022

STATUS

editing

proposed

#13 by Ilya Gutkovskiy at Sat Jun 25 03:53:12 EDT 2022

FORMULA

E.g.f.: (exp(x) - Sum_{k=0..3} x^k/k!) * exp(exp(x) - 1). - Ilya Gutkovskiy, Jun 25 2022

STATUS

approved

editing

#12 by Alois P. Heinz at Thu Jan 06 14:53:19 EST 2022

STATUS

editing

approved

#11 by Alois P. Heinz at Thu Jan 06 14:53:17 EST 2022

MAPLE

# second Maple program:

b:= proc(n) option remember; `if`(n=0, [1, 0], add((p-> p+[0,

`if`(j>3, p[1], 0)])(b(n-j)*binomial(n-1, j-1)), j=1..n))

end:

a:= n-> b(n)[2]:

seq(a(n), n=4..30); # Alois P. Heinz, Jan 06 2022

STATUS

approved

editing

#10 by Bruno Berselli at Mon May 28 03:26:06 EDT 2018

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reviewed

approved

#9 by Michel Marcus at Mon May 28 01:47:54 EDT 2018

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proposed

reviewed

#8 by Jean-François Alcover at Mon May 28 01:46:51 EDT 2018

STATUS

editing

proposed

#7 by Jean-François Alcover at Mon May 28 01:46:49 EDT 2018

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 *)

STATUS

approved

editing