%I #7 Aug 11 2024 10:34:49

%S 1,0,0,1,2,24,0,4,672,358560,1,20,38976,476850240,20911317073920,0,

%T 100,3550848,1304813266560,2432400136566865920,

%U 15510918113914245120000000,1,620,471899904,6394544826128640,620390024129961834577920,265250998502017388926894080000000,371993135808163790752351286618750976000000

%N Triangle read by rows, T(n,k) = Sum_{i=0..n} (-1)^i*(k!)^i*(n*k-i*k)!), 0<=k<=n.

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

%H Milan Janjić, <a href="https://web.archive.org/web/20130527052801/http://www.pmfbl.org/janjic/enumfun.pdf">Enumerative Formulae for Some Functions on Finite Sets</a>.

%e The triangle begins

%e 1,

%e 0, 0,

%e 1, 2, 24,

%e 0, 4, 672, 358560,

%e 1, 20, 38976, 476850240, 20911317073920,

%e 0, 100, 3550848, 1304813266560, 2432400136566865920, 15510918113914245120000000,

%e ...

%Y Cf. A153229 (column 1).

%K nonn,tabl

%O 0,5

%A _Hugo Pfoertner_, Aug 11 2024