A025040 Number of partitions of { 1, 2, ..., 8n } into sets of size 8.

1, 1, 6435, 1577585295, 4148378852099625, 63805953776276649848625, 4012852078114749147678149338875, 814318942973348333484015877548157809375, 450538787986875167583433232345723106006796340625, 599167346385710947364525167684682505182168120225201390625

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• 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=8 of A060540.

Programs

Mathematica

Table[Pochhammer[n + 1, 7*n]/8!^n, {n, 0, 10}] (* Paolo Xausa, Aug 08 2024 *)

Formula

a(n) = (8n)!/(n!(8!)^n). - Christian G. Bower, Sep 15 1998

a(n) ~ 2^(17*n+3/2) * (n/e)^(7*n) / 315^n. - Amiram Eldar, Aug 28 2025

Extensions

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