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 A134737 Number of partitions of the n-th partition number into positive parts not greater than n. 3

%I

%S 1,2,3,6,13,44,131,638,3060,22367,167672,2127747,26391031,537973241,

%T 12274276512,429819314124,16928838590640,1068323095351171,

%U 75345432929798690,8339062208354516217,1083103359596125913021,209256696715820656730807,48414226122932084106352434

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

%H Alois P. Heinz, <a href="/A134737/b134737.txt">Table of n, a(n) for n = 1..55</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Partition.html">Partition</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>

%H <a href="/index/Par#partN">Index entries for sequences related to partitions</a>

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

%p 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

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

%t 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_ *)

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 07 2007

%E More terms from _Alois P. Heinz_, Jul 17 2009

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Last modified December 9 21:09 EST 2018. Contains 318023 sequences. (Running on oeis4.)