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Number of partitions of { 1, 2, ..., 7n } into sets of size 7.
2

%I #28 May 31 2023 09:50:30

%S 1,1716,66512160,19688264481600,26478825654361766400,

%T 119059073926364394099763200,1461034854396267778567973305958400,

%U 42354925592620124113657511548409579520000

%N Number of partitions of { 1, 2, ..., 7n } into sets of size 7.

%H Vincenzo Librandi, <a href="/A025039/b025039.txt">Table of n, a(n) for n = 1..80</a>

%H Cyril Banderier, Philippe Marchal, 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) = (7n)!/(n!(7!)^n). - _Christian G. Bower_, Sep 15 1998

%t Table[(7n)!/(n!(7!)^n),{n,1,10}] (* _Vincenzo Librandi_, Jun 26 2012 *)

%o (Sage) [rising_factorial(n+1,6*n)/5040^n for n in (0..15)] # _Peter Luschny_, Jun 26 2012

%o (Magma)[Factorial(7*n)/(Factorial(n)*Factorial(7)^n): n in [1..10]] // _Vincenzo Librandi_, Jun 26 2012

%Y Column k=7 of A060540.

%K nonn

%O 1,2

%A _David W. Wilson_