%I #38 Aug 08 2024 11:05:10
%S 1,1,462,2858856,96197645544,11423951396577720,3708580189773818399040,
%T 2779202577056119960603777920,4263127221846887596248598498826880,
%U 12233832241625685631640659383106015132800,61247286460823449786646954166350590676638060800
%N Number of partitions of { 1, 2, ..., 6n } into sets of size 6.
%H Andrew Howroyd, <a href="/A025038/b025038.txt">Table of n, a(n) for n = 0..50</a>
%H Cyril Banderier, Philippe Marchal, and Michael Wallner, <a href="https://arxiv.org/abs/1805.09017">Rectangular Young tableaux with local decreases and the density method for uniform random generation</a> (short version), arXiv:1805.09017 [cs.DM], 2018.
%H Robert Coquereaux and Jean-Bernard Zuber, <a href="https://arxiv.org/abs/2305.01100">Counting partitions by genus. II. A compendium of results</a>, arXiv:2305.01100 [math.CO], 2023. See p. 17.
%F a(n) = (6n)!/(n!(6!)^n). - _Christian G. Bower_, Sep 15 1998
%t Table[Pochhammer[n + 1, 5*n]/6!^n, {n, 0, 15}] (* _Paolo Xausa_, Aug 08 2024 *)
%o (Sage) [rising_factorial(n+1,5*n)/720^n for n in (0..15)] # _Peter Luschny_, Jun 26 2012
%Y Column k=6 of A060540.
%K nonn
%O 0,3
%A _David W. Wilson_
%E a(0) and a(10) from _Andrew Howroyd_, Feb 26 2018