A025038 Number of partitions of { 1, 2, ..., 6n } into sets of size 6.

1, 1, 462, 2858856, 96197645544, 11423951396577720, 3708580189773818399040, 2779202577056119960603777920, 4263127221846887596248598498826880, 12233832241625685631640659383106015132800, 61247286460823449786646954166350590676638060800

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.
• Robert Coquereaux and Jean-Bernard Zuber, Counting partitions by genus. II. A compendium of results, arXiv:2305.01100 [math.CO], 2023. See p. 17.

Crossrefs

Column k=6 of A060540.

Programs

Mathematica

Table[Pochhammer[n + 1, 5*n]/6!^n, {n, 0, 15}] (* Paolo Xausa, Aug 08 2024 *)

Sage

[rising_factorial(n+1,5*n)/720^n for n in (0..15)] # Peter Luschny, Jun 26 2012

Formula

a(n) = (6n)!/(n!(6!)^n). - Christian G. Bower, Sep 15 1998

a(n) ~ 2^(2*n+1/2) * 3^(4*n+1/2) * (n/e)^(5*n) / 5^n. - Amiram Eldar, Aug 28 2025

Extensions

a(0) and a(10) from Andrew Howroyd, Feb 26 2018