A025039 Number of partitions of { 1, 2, ..., 7n } into sets of size 7.

1, 1716, 66512160, 19688264481600, 26478825654361766400, 119059073926364394099763200, 1461034854396267778567973305958400, 42354925592620124113657511548409579520000

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..80

Cyril Banderier, Philippe Marchal, 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) = (7n)!/(n!(7!)^n). - Christian G. Bower, Sep 15 1998

Mathematica

Table[(7n)!/(n!(7!)^n), {n, 1, 10}] (* Vincenzo Librandi, Jun 26 2012 *)

Prog

(Sage) [rising_factorial(n+1, 6*n)/5040^n for n in (0..15)] # Peter Luschny, Jun 26 2012
(Magma)[Factorial(7*n)/(Factorial(n)*Factorial(7)^n): n in [1..10]] // Vincenzo Librandi, Jun 26 2012

Crossrefs

Column k=7 of A060540.

Sequence in context: A208620 A365027 A294854 * A068303 A212929 A252610

Adjacent sequences: A025036 A025037 A025038 * A025040 A025041 A025042

Keyword

nonn

Author

David W. Wilson

Status

approved