A237998 Number of partitions of 2^n into parts that are at most n.

0, 1, 3, 10, 64, 831, 26207, 2239706, 567852809, 454241403975, 1192075219982204, 10510218491798860052, 315981966712495811700951, 32726459268483342710907384794, 11771239570056489326716955796095261, 14808470136486015545654676685321653888199

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..62

A. V. Sills and D. Zeilberger, Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz) (arXiv:1108.4391 [math.CO])

Formula

a(n) = [x^(2^n)] Product_{j=1..n} 1/(1-x^j).

a(n) ~ 2^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015

Example

a(1) = 1: 11.
a(2) = 3: 22, 211, 1111.
a(3) = 10: 332, 2222, 3221, 3311, 22211, 32111, 221111, 311111, 2111111, 11111111.

Mathematica

a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, 2^n}];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Nov 03 2018 *)

Crossrefs

Column k=2 of A238010.

Cf. A236810, A237512, A237999, A238000, A238001, A258672.

Sequence in context: A042705 A041014 A367641 * A167939 A352766 A206724

Adjacent sequences: A237995 A237996 A237997 * A237999 A238000 A238001

Keyword

nonn

Author

Alois P. Heinz, Feb 16 2014

Status

approved