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Number of partitions of { 1, 2, ..., 5n } into sets of size 5.
5

%I #37 May 26 2023 01:02:58

%S 1,1,126,126126,488864376,5194672859376,123378675083039376,

%T 5721809435651034101376,470624547891733205872277376,

%U 63887753000850674430367526069376,13536281554808237495608549953475109376

%N Number of partitions of { 1, 2, ..., 5n } into sets of size 5.

%H Vincenzo Librandi, <a href="/A025037/b025037.txt">Table of n, a(n) for n = 0..100</a> (term a(0) added by Sidney Cadot)

%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) = (5n)!/(n!(5!)^n). - _Christian G. Bower_, Sep 15 1998

%t Table[(5n)!/(n!(5!)^n),{n,1,10}] (* _Vincenzo Librandi_, Jun 26 2012 *)

%o (Sage) [rising_factorial(n+1,4*n)/120^n for n in (0..15)] # _Peter Luschny_, Jun 26 2012

%o (Magma) [Factorial(5*n)/(Factorial(n)*Factorial(5)^n): n in [1..10]] // _Vincenzo Librandi_, Jun 26 2012

%Y Column k=5 of A060540.

%K nonn

%O 0,3

%A _David W. Wilson_

%E a(0) from _Peter Luschny_, Apr 24 2023