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

0,5

Comments

For a combinatorial interpretation see Janjić, page 10, corollary 3.6.

Links

Table of n, a(n) for n=0..27.

Milan Janjić, Enumerative Formulae for Some Functions on Finite Sets.

Example

The triangle begins
  1,
  0,   0,
  1,   2,      24,
  0,   4,     672,        358560,
  1,  20,   38976,     476850240,      20911317073920,
  0, 100, 3550848, 1304813266560, 2432400136566865920, 15510918113914245120000000,
  ...

Crossrefs

Cf. A153229 (column 1).

Sequence in context: A228241 A054909 A171636 * A350257 A270562 A100816

Adjacent sequences: A375301 A375302 A375303 * A375305 A375306 A375307

Keyword

nonn,tabl

Author

Hugo Pfoertner, Aug 11 2024

Status

approved