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URL: https://oeis.org/A025037

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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, 4280862577989659916223699531336456815269376
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.
Bishal Deb and Alan D. Sokal, Higher-order Stirling cycle and subset triangles: Total positivity, continued fractions and real-rootedness, arXiv:2507.18959 [math.CO], 2025. See p. 7.
FORMULA
a(n) = (5n)!/(n!(5!)^n). - Christian G. Bower, Sep 15 1998
a(n) ~ 5^(4*n+1/2) * (n/e)^(4*n) / 24^n. - Amiram Eldar, Aug 28 2025
MATHEMATICA
Table[(5n)!/(n!(5!)^n), {n, 0, 10}] (* Vincenzo Librandi, Jun 26 2012 *)
PROG
(SageMath) [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 [0..10]]; // Vincenzo Librandi, Jun 26 2012
CROSSREFS
Column k=5 of A060540.
Sequence in context: A365026 A294852 A078206 * A281478 A381866 A381533
KEYWORD
nonn
EXTENSIONS
a(0) from Peter Luschny, Apr 24 2023
STATUS
approved