A238000 Number of partitions of n^n into parts that are at most n.

0, 1, 3, 75, 123464, 33432635477, 2561606354507677872, 85980297709044488588773397089, 1841159754991692001851990839259642586671980, 34687845413783594101366282545316028561007822069601179170488

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..27

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

a(n) ~ exp(2*n) * n^(n*(n-3)) / (2*Pi). - Vaclav Kotesovec, May 25 2015

Example

a(1) = 1: 1.
a(2) = 3: 22, 211, 1111.
a(3) = 75: 333333333, ..., 111111111111111111111111111.

Mathematica

a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, n^n}];
a[0] = 0;
Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Nov 03 2018 *)

Crossrefs

Main diagonal of A238010 and A238016.

Cf. A236810, A237512, A237998, A237999, A238001.

Sequence in context: A336062 A320306 A359500 * A308866 A089301 A037110

Adjacent sequences: A237997 A237998 A237999 * A238001 A238002 A238003

Keyword

nonn

Author

Alois P. Heinz, Feb 16 2014

Status

approved