A258670 Number of partitions of (2*n)! into parts that are at most n.

0, 1, 13, 43561, 455366036161, 60209252317216962943201, 291857679749953126623181556402787323521, 120972618144269517756284629487432992029777542693069847287041

Offset: 0

Author

Vaclav Kotesovec, Jun 07 2015

Keywords

• nonn

Comments

Conjecture: If f(n) >= O(n^4) then "number of partitions of f(n) into parts that are at most n" is asymptotic to f(n)^(n-1) / (n!*(n-1)!). For the examples see A238016 and A238010.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..21
• G. J. Rieger, Über Partitionen, Mathematische Annalen (1959), Volume: 138, page 356-362
• 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])

Crossrefs

Cf. A236810, A237998, A238000, A238010, A238016, A258668, A258669, A258671.

Formula

a(n) ~ (2*n)!^(n-1) / (n!*(n-1)!).