A025041 Number of partitions of { 1, 2, ..., 9n } into sets of size 9.

1, 1, 24310, 37978905250, 893864677761055000, 158421985022100255941485000, 140413003088367308737750586624350000, 474750200441159213998774295008486246570750000, 5050927030108676304976606530597710043478228399030000000

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy
• changed

Links

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

Crossrefs

Column k=9 of A060540.

Programs

Mathematica

Table[Pochhammer[n + 1, 8*n]/9!^n, {n, 0, 10}] (* Paolo Xausa, Aug 08 2024 *)

Formula

a(n) = (9*n)!/(n!*(9!)^n). - Christian G. Bower, Sep 15 1998

a(n) ~ 3^(14*n+1) * (n/e)^(8*n) / 4480^n. - Amiram Eldar, Aug 28 2025

Extensions

a(0)=1 from Andrew Howroyd, Feb 26 2018