A239169 Number of partitions of 10^n into parts that are at most n with at least one part of each size.

0, 1, 49, 82834, 6934032777, 34711806631898612, 11573466447067793596124382, 275570877432663678053361428346732364, 492094366103239904094628894222685729680850442491, 68346513550765879549763426703232180189170804739067223698078512

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..33

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^(10^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).

a(n) ~ 10^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015

Crossrefs

Column k=10 of A238012.

Sequence in context: A100418 A369698 A351443 * A134725 A203499 A013843

Adjacent sequences: A239166 A239167 A239168 * A239170 A239171 A239172

Keyword

nonn

Author

Alois P. Heinz, Mar 11 2014

Status

approved