The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A050343 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A050343

Number of partitions of n into distinct parts with 2 levels of parentheses.
(history; published version)

#16 by Joerg Arndt at Sat Dec 19 14:18:57 EST 2015

STATUS

proposed

approved

#15 by Jon E. Schoenfield at Sat Dec 19 13:27:54 EST 2015

STATUS

editing

proposed

#14 by Jon E. Schoenfield at Sat Dec 19 13:27:53 EST 2015

EXAMPLE

4 = ((4)) = ((3))+((1)) = ((3)+(1)) = ((3+1)) = ((2+1))+((1)) = ((2+1)+(1)).

AUTHOR

Christian G. Bower, Oct 15 1999.

STATUS

approved

editing

#13 by Bruno Berselli at Fri Jul 17 06:11:58 EDT 2015

STATUS

proposed

approved

#12 by Jean-François Alcover at Fri Jul 17 05:58:46 EDT 2015

STATUS

editing

proposed

#11 by Jean-François Alcover at Fri Jul 17 05:58:14 EDT 2015

MATHEMATICA

g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, g[n, i-1] + If[i>n, 0, g[n-i, i-1]]]] ; h[n_, i_] := h[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[g[i, i], j]*h[n-i*j, i-1], {j, 0, n/i}]]]; b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[ Binomial[ h[i, i], j]*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 17 2015, after Alois P. Heinz *)

STATUS

approved

editing

#10 by Alois P. Heinz at Sun May 19 21:18:52 EDT 2013

STATUS

editing

approved

#9 by Alois P. Heinz at Sun May 19 20:34:41 EDT 2013

LINKS

N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

MAPLE

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

g(n, i-1)+`if`(i>n, 0, g(n-i, i-1))))

end:

h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(binomial(g(i, i), j)*h(n-i*j, i-1), j=0..n/i)))

end:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(binomial(h(i, i), j)*b(n-i*j, i-1), j=0..n/i)))

end:

a:= n-> b(n, n):

seq(a(n), n=0..50); # Alois P. Heinz, May 19 2013

#8 by Alois P. Heinz at Sun May 19 20:32:09 EDT 2013

LINKS

Alois P. Heinz, <a href="/A050343/b050343.txt">Table of n, a(n) for n = 0..1000</a>

#7 by Alois P. Heinz at Sun May 19 20:13:38 EDT 2013

DATA

1, 1, 1, 4, 7, 14, 29, 57, 110, 217, 417, 794, 1513, 2860, 5373, 10063, 18740, 34750, 64221, 118199, 216775, 396297, 722136, 1311888, 2376575, 4293407, 7735941, 13903985, 24929763, 44595606, 79598328, 141770576, 251984463, 446991405, 791391545, 1398551523

STATUS

approved

editing