A132641 Number of partitions of n, p(n), raised to power p(n).

1, 1, 4, 27, 3125, 823543, 285311670611, 437893890380859375, 341427877364219557396646723584, 205891132094649000000000000000000000000000000, 150130937545296572356771972164254457814047970568738777235893533016064

Offset: 0

Author

Omar E. Pol, Aug 24 2007

Keywords

• nonn

Comments

a(n) is also the number of endofunctions on the partitions of n. - Max Sills, Feb 07 2012

Examples

			a(5) = 823543 because p(5) = 7 and we can write 823543 = 7^7 or 823543 = 7*7*7*7*7*7*7.
		

Crossrefs

Cf. A000041, A000312, A008973, A008974, A051674.

Programs

Maple

a:= n-> (p-> p^p)(combinat[numbpart](n)):
seq(a(n), n=0..11);  # Alois P. Heinz, Nov 04 2024

Mathematica

Table[ PartitionsP@n ^ PartitionsP@n, {n, 10}] (* Robert G. Wilson v, Aug 28 2007 *)

Formula

a(n) = p(n)^p(n).

a(n) = A000312(A000041(n)). - Alois P. Heinz, Nov 04 2024

Extensions

More terms from Robert G. Wilson v, Aug 28 2007

a(0)=1 prepended by Alois P. Heinz, Nov 04 2024