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A050343 Number of partitions of n into distinct parts with 2 levels of parentheses. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

FORMULA

Weigh transform of A050342.

EXAMPLE

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

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

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-Fran├žois Alcover, Jul 17 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A050342-A050350.

Sequence in context: A094968 A049946 A076975 * A245002 A199628 A049945

Adjacent sequences:  A050340 A050341 A050342 * A050344 A050345 A050346

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1999

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)