OFFSET
1,5
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) = k*(n-1)! - k!.
Sum_{k=1..n} T(n, k) = ((n+1)! - 2*!(n+1))/2 = (A000142(n+1) - 2*(A003422(n+1) -1))/2 = (A000142(n+1) - 2*(A007489(n) - 2))/2. - G. C. Greubel, Apr 10 2021
EXAMPLE
Triangle begins as:
0;
0, 0;
1, 2, 0;
5, 10, 12, 0;
23, 46, 66, 72, 0;
119, 238, 354, 456, 480, 0;
719, 1438, 2154, 2856, 3480, 3600, 0;
5039, 10078, 15114, 20136, 25080, 29520, 30240, 0;
40319, 80638, 120954, 161256, 201480, 241200, 277200, 282240, 0;
362879, 725758, 1088634, 1451496, 1814280, 2176560, 2535120, 2862720, 2903040, 0;
MAPLE
A137260:= (n, k) -> k*((n-1)! - (k-1)!); seq(seq(A137260(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 10 2021
MATHEMATICA
T[n_, k_]:= k*(n-1)! - k!;
Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 10 2021 *)
PROG
(Magma) [k*Factorial(n-1) - Factorial(k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 10 2021
(Sage) flatten([[k*factorial(n-1) - factorial(k) 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