OFFSET
0,5
COMMENTS
a(n) is the number of partitions of n! - n*(n+1)/2 into parts that are at most n. - Alois P. Heinz, Feb 08 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..31
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])
StackExchange, Combinations sum_{k=1..m} k*n_k = m!, Jan 29 2014
FORMULA
a(n) = [x^(n!)] Product_{k=1..n} x^k/(1-x^k).
a(n) = [x^(n!-n*(n+1)/2)] Product_{k=1..n} 1/(1-x^k). - Alois P. Heinz, Feb 08 2014
a(n) ~ n * (n!)^(n-3) ~ n^(n^2-5*n/2-1/2) * (2*Pi)^((n-3)/2) / exp(n*(n-3)-1/12). - Vaclav Kotesovec, Jun 05 2015
MATHEMATICA
Table[Coefficient[Series[Product[x^k/(1-x^k), {k, n}], {x, 0, n!}], x^(n!) ] , {n, 7}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Feb 08 2014
EXTENSIONS
a(8)-a(11) from Alois P. Heinz, Feb 08 2014
STATUS
approved