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URL: https://oeis.org/A025038

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A025038
Number of partitions of { 1, 2, ..., 6n } into sets of size 6.
3
1, 1, 462, 2858856, 96197645544, 11423951396577720, 3708580189773818399040, 2779202577056119960603777920, 4263127221846887596248598498826880, 12233832241625685631640659383106015132800, 61247286460823449786646954166350590676638060800
OFFSET
0,3
LINKS
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.
Bishal Deb and Alan D. Sokal, Higher-order Stirling cycle and subset triangles: Total positivity, continued fractions and real-rootedness, arXiv:2507.18959 [math.CO], 2025. See p. 7.
FORMULA
a(n) = (6n)!/(n!(6!)^n). - Christian G. Bower, Sep 15 1998
a(n) ~ 2^(2*n+1/2) * 3^(4*n+1/2) * (n/e)^(5*n) / 5^n. - Amiram Eldar, Aug 28 2025
From Peter Bala, Dec 13 2025: (Start)
a(n) = (1/10)*(2*n - 1)*(3*n - 1)*(3*n - 2)*(6*n - 1)*(6*n - 5)*a(n-1) with a(0) = 1.
G.f.: exp(x^6/6!) = 1 + x^6/6! + 462*x^12/12! + 2858856*x^18/18! + .... (End)
MATHEMATICA
Table[Pochhammer[n + 1, 5*n]/6!^n, {n, 0, 15}] (* Paolo Xausa, Aug 08 2024 *)
PROG
(SageMath) [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
KEYWORD
nonn,easy
EXTENSIONS
a(0) and a(10) from Andrew Howroyd, Feb 26 2018
STATUS
approved