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A025037
Number of partitions of { 1, 2, ..., 5n } into sets of size 5.
5
1, 1, 126, 126126, 488864376, 5194672859376, 123378675083039376, 5721809435651034101376, 470624547891733205872277376, 63887753000850674430367526069376, 13536281554808237495608549953475109376
OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100 (term a(0) added by Sidney Cadot)
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.
FORMULA
a(n) = (5n)!/(n!(5!)^n). - Christian G. Bower, Sep 15 1998
MATHEMATICA
Table[(5n)!/(n!(5!)^n), {n, 1, 10}] (* Vincenzo Librandi, Jun 26 2012 *)
PROG
(Sage) [rising_factorial(n+1, 4*n)/120^n for n in (0..15)] # Peter Luschny, Jun 26 2012
(Magma) [Factorial(5*n)/(Factorial(n)*Factorial(5)^n): n in [1..10]] // Vincenzo Librandi, Jun 26 2012
CROSSREFS
Column k=5 of A060540.
Sequence in context: A365026 A294852 A078206 * A281478 A212927 A300785
KEYWORD
nonn
EXTENSIONS
a(0) from Peter Luschny, Apr 24 2023
STATUS
approved