OFFSET
1,4
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
Krassimir Penev, The Fubini Principle, The American Mathematical Monthly, Vol. 115, No. 3 (Mar., 2008), pp. 245-248.
FORMULA
T(n, k) = n! - n*(k-1)!.
Sum_{k=1..n} T(n, k) = n*(n! - !n) = n*(n! - A003422(n)). - G. C. Greubel, Apr 10 2021
EXAMPLE
Triangle begins as:
0;
0, 0;
3, 3, 0;
20, 20, 16, 0;
115, 115, 110, 90, 0;
714, 714, 708, 684, 576, 0;
5033, 5033, 5026, 4998, 4872, 4200, 0;
40312, 40312, 40304, 40272, 40128, 39360, 34560, 0;
362871, 362871, 362862, 362826, 362664, 361800, 356400, 317520, 0;
MAPLE
A137259:= (n, k) -> n*((n-1)! - (k-1)!); seq(seq(A137259(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 10 2021
MATHEMATICA
T[n_, k_]:= n! - n*(k-1)!;
Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 10 2021 *)
PROG
(Magma) [n*(Factorial(n-1) - Factorial(k-1)): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2021
(Sage) flatten([[n*(factorial(n-1) - factorial(k-1)) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 10 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 11 2008
EXTENSIONS
Edited by G. C. Greubel, Apr 10 2021
STATUS
approved