A025037 Number of partitions of { 1, 2, ..., 5n } into sets of size 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

Adjacent sequences: A025034 A025035 A025036 * A025038 A025039 A025040

Keyword

nonn

Author

David W. Wilson

Extensions

a(0) from Peter Luschny, Apr 24 2023

Status

approved