A025038 Number of partitions of { 1, 2, ..., 6n } into sets of size 6.

1, 1, 462, 2858856, 96197645544, 11423951396577720, 3708580189773818399040, 2779202577056119960603777920, 4263127221846887596248598498826880, 12233832241625685631640659383106015132800, 61247286460823449786646954166350590676638060800

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

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) = (6n)!/(n!(6!)^n). - Christian G. Bower, Sep 15 1998

Prog

(Sage) [rising_factorial(n+1, 5*n)/720^n for n in (0..15)] # Peter Luschny, Jun 26 2012

Crossrefs

Column k=6 of A060540.

Sequence in context: A295432 A213406 A294853 * A028684 A212928 A102997

Adjacent sequences: A025035 A025036 A025037 * A025039 A025040 A025041

Keyword

nonn

Author

David W. Wilson

Extensions

a(0) and a(10) from Andrew Howroyd, Feb 26 2018

Status

approved