A375304 Triangle read by rows, T(n,k) = Sum_{i=0..n} (-1)^i*(k!)^i*(n*k-i*k)!, 0<=k<=n.
1, 0, 0, 1, 2, 24, 0, 4, 672, 358560, 1, 20, 38976, 476850240, 20911317073920, 0, 100, 3550848, 1304813266560, 2432400136566865920, 15510918113914245120000000, 1, 620, 471899904, 6394544826128640, 620390024129961834577920, 265250998502017388926894080000000, 371993135808163790752351286618750976000000
Offset: 0
Examples
The triangle begins 1, 0, 0, 1, 2, 24, 0, 4, 672, 358560, 1, 20, 38976, 476850240, 20911317073920, 0, 100, 3550848, 1304813266560, 2432400136566865920, 15510918113914245120000000, ...
Links
- Milan Janjić, Enumerative Formulae for Some Functions on Finite Sets.
Crossrefs
Cf. A153229 (column 1).
Comments