A134737 Number of partitions of the n-th partition number into positive parts not greater than n.

1, 2, 3, 6, 13, 44, 131, 638, 3060, 22367, 167672, 2127747, 26391031, 537973241, 12274276512, 429819314124, 16928838590640, 1068323095351171, 75345432929798690, 8339062208354516217, 1083103359596125913021, 209256696715820656730807, 48414226122932084106352434

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..55

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-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Crossrefs

Sequence in context: A135967 A290248 A146000 * A030733 A335288 A122839

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