OFFSET
0,1
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k).
Sum_{k=0..n} T(n, k) = 2*n! + A342111(n). - G. C. Greubel, Jun 05 2021
EXAMPLE
3;
1, 1;
1, 3, 1;
1, 11, 11, 1;
1, 48, 143, 48, 1;
1, 274, 1835, 1835, 274, 1;
1, 1935, 23649, 51075, 23649, 1935, 1;
1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1;
1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1;
MATHEMATICA
T[n_, k_] = (-1)^(n-k)*StirlingS1[n, k] + (-1)^k*StirlingS1[n, 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)
A155744:= func< n, k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) + (-1)^k*StirlingFirst(n, n-k) + (-1)^(n-k)*StirlingFirst(n, k) >;
[A155744(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 05 2021
(Sage)
def A155744(n, k): return stirling_number1(n, k)*stirling_number1(n, n-k) + stirling_number1(n, k) + stirling_number1(n, n-k)
flatten([[A155744(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