A283111 Number of partitions of 2^n into n parts.

0, 1, 2, 5, 34, 480, 17180, 1652171, 461346215, 396507897335, 1093817527528804, 9967640563717565125, 306039783996035518230753, 32112037153481933712774822566, 11641561173234351448063113301394401, 14714021393940105546041647309452434048219, 65349955097974241266907510524139945537027169461

Offset: 0

Author

Francois Alcover, Feb 28 2017

Keywords

• nonn

Crossrefs

Cf. A008284.

Programs

Mathematica

a[n_] := SeriesCoefficient[1/Product[1 - x^k, {k, 1, n}], {x, 0, 2^n - n}]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 14}] (* Jean-François Alcover, Mar 01 2017 *)

Sage

def a283111(n): return Partitions(2**n, length=n).cardinality() # Max Alekseyev, Apr 07 2025

Formula

a(n) = P(2^n,n), where P(x, y) is the number of partitions of x into y parts.

a(n) = A008284(2^n,n). - R. J. Mathar, Mar 10 2017

Extensions

a(15)-a(16) from Max Alekseyev, Apr 07 2025