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A238000 Number of partitions of n^n into parts that are at most n. 11
0, 1, 3, 75, 123464, 33432635477, 2561606354507677872, 85980297709044488588773397089, 1841159754991692001851990839259642586671980, 34687845413783594101366282545316028561007822069601179170488 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 03 2018 *)

CROSSREFS

Main diagonal of A238010 and A238016.

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

Sequence in context: A183290 A336062 A320306 * A308866 A089301 A037110

Adjacent sequences:  A237997 A237998 A237999 * A238001 A238002 A238003

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 16 2014

STATUS

approved

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Last modified July 31 01:15 EDT 2021. Contains 346365 sequences. (Running on oeis4.)