A025042 Number of partitions of { 1, 2, ..., 10n } into sets of size 10.

1, 1, 92378, 925166131890, 196056702961398759480, 402789797982510165934296910320, 5061324188732823772720935900249118313520, 286835743456312434671347570864365730919777702885760, 59034098562652855324502713832050720577190114808212674462486400

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• changed

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Cyril Banderier, Philippe Marchal, and Michael Wallner, Rectangular Young tableaux with local decreases and the density method for uniform random generation (short version), arXiv:1805.09017 [cs.DM], 2018.

Crossrefs

Column k=10 of A060540.

Programs

Mathematica

Table[Pochhammer[n + 1, 9*n]/10!^n, {n, 0, 10}] (* Paolo Xausa, Aug 08 2024 *)

Formula

a(n) = (10n)!/(n!(10!)^n). - Christian G. Bower, Sep 15 1998

a(n) = a(n-1)*binomial(10*n-1,9). - Christian Krause, Dec 07 2023

a(n) ~ 2^(2*n+1/2) * 5^(8*n+1/2) * (n/e)^(9*n) / 567^n. - Amiram Eldar, Aug 28 2025

Extensions

a(0)=1 from Andrew Howroyd, Feb 26 2018