A025037 Number of partitions of { 1, 2, ..., 5n } into sets of size 5.
1, 1, 126, 126126, 488864376, 5194672859376, 123378675083039376, 5721809435651034101376, 470624547891733205872277376, 63887753000850674430367526069376, 13536281554808237495608549953475109376, 4280862577989659916223699531336456815269376
Offset: 0
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.
Crossrefs
Column k=5 of A060540.
Programs
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Magma
[Factorial(5*n)/(Factorial(n)*Factorial(5)^n): n in [0..10]]; // Vincenzo Librandi, Jun 26 2012
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Mathematica
Table[(5n)!/(n!(5!)^n),{n,0,10}] (* Vincenzo Librandi, Jun 26 2012 *) -
Sage
[rising_factorial(n+1,4*n)/120^n for n in (0..15)] # Peter Luschny, Jun 26 2012
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
Extensions
a(0) from Peter Luschny, Apr 24 2023