OFFSET
0,8
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle flattened
FORMULA
T(n, k) = (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k).
Sum_{k=0..n} T(n, k) = A342111(n). - G. C. Greubel, Jun 05 2021
EXAMPLE
Triangle begins as:
1;
0, 0;
0, 1, 0;
0, 6, 6, 0;
0, 36, 121, 36, 0;
0, 240, 1750, 1750, 240, 0;
0, 1800, 23290, 50625, 23290, 1800, 0;
0, 15120, 308700, 1193640, 1193640, 308700, 15120, 0;
0, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 0;
MATHEMATICA
T[n_, k_]:= (-1)^n*StirlingS1[n, k]*StirlingS1[n, n-k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 05 2021 *)
PROG
(Magma)
A155742:= func< n, k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) >;
[A155742(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 05 2021
(Sage)
def A155742(n, k): return stirling_number1(n, k)*stirling_number1(n, n-k)
flatten([[A155742(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 05 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jan 26 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 05 2021
STATUS
approved