A132641 - OEIS

A132641

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

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

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OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..10.

FORMULA

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

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

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A249110 A348329 A051674 * A008973 A132646 A254866

Adjacent sequences: A132638 A132639 A132640 * A132642 A132643 A132644

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 24 2007

EXTENSIONS

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

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

STATUS

approved