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A134737 Number of partitions of the n-th partition number into positive parts not greater than n. 3
1, 2, 3, 6, 13, 44, 131, 638, 3060, 22367, 167672, 2127747, 26391031, 537973241, 12274276512, 429819314124, 16928838590640, 1068323095351171, 75345432929798690, 8339062208354516217, 1083103359596125913021, 209256696715820656730807, 48414226122932084106352434 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Partition

Eric Weisstein's World of Mathematics, Partition Function P

Index entries for sequences related to partitions

FORMULA

a(n) = A026820(A026820(n,n),n) = A026820(A000041(n),n).

MAPLE

with (numtheory): P:= proc(n) local d, j; P(n):= `if`(n=0, 1, add (add (d, d=divisors(j)) *P(n-j), j=1..n)/n) end: b:= proc(n, i) if n<0 then 0 elif n=0 then 1 elif i=0 then 0 else b(n, i):= b(n, i-1) +b(n-i, i) fi end: a:= n-> b(P(n), n): seq (a(n), n=1..25); # Alois P. Heinz, Jul 17 2009

MATHEMATICA

(* first do *) Needs["DiscreteMath`IntegerPartitions`"] (* then *) a[n_] := Length@ IntegerPartitions[ PartitionsP[n], n] (* Robert G. Wilson v, Nov 11 2007 *)

P[n_] := P[n] = Module[{d, j}, If[n == 0, 1, Sum[DivisorSum[j, #&]*P[n - j], {j, 1, n}]/n]]; b [n_, i_] := b[n, i] = Which[n<0, 0, n == 0, 1, i == 0, 0, True, b[n, i] = b[n, i-1] + b[n-i, i]]; a[n_] := b[P[n], n]; Table [a[n], {n, 1, 25}] (* Jean-Fran├žois Alcover, Nov 11 2015, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A135967 A290248 A146000 * A030733 A122839 A258077

Adjacent sequences:  A134734 A134735 A134736 * A134738 A134739 A134740

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 07 2007

EXTENSIONS

More terms from Alois P. Heinz, Jul 17 2009

STATUS

approved

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Last modified August 19 16:24 EDT 2017. Contains 290809 sequences.