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

Author

Reinhard Zumkeller, Nov 07 2007

Keywords

• nonn

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

Programs

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 *)

Formula

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

Extensions

More terms from Alois P. Heinz, Jul 17 2009