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

1, 1716, 66512160, 19688264481600, 26478825654361766400, 119059073926364394099763200, 1461034854396267778567973305958400, 42354925592620124113657511548409579520000, 2603748678087112079607396853175424115984250880000, 312130809252424791883997487259425015552026787308175360000

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• changed

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.

Crossrefs

Column k=7 of A060540.

Programs

Magma

[Factorial(7*n)/(Factorial(n)*Factorial(7)^n): n in [0..10]]; // Vincenzo Librandi, Jun 26 2012

Mathematica

Table[(7n)!/(n!(7!)^n),{n,0,10}] (* Vincenzo Librandi, Jun 26 2012 *)

Sage

[rising_factorial(n+1,6*n)/5040^n for n in (0..15)] # Peter Luschny, Jun 26 2012

Formula

a(n) = (7n)!/(n!(7!)^n). - Christian G. Bower, Sep 15 1998

a(n) ~ 7^(6*n+1/2) * (n/e)^(6*n) / 720^n. - Amiram Eldar, Aug 28 2025