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A155825
Triangle T(n, k) = (-1)^n * n! * StirlingS1(n, k)*StirlingS1(n, n-k)/binomial(n, k), read by rows.
1
1, 0, 0, 0, 1, 0, 0, 12, 12, 0, 0, 216, 484, 216, 0, 0, 5760, 21000, 21000, 5760, 0, 0, 216000, 1117920, 1822500, 1117920, 216000, 0, 0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0, 0, 711244800, 6059370240, 18531878400, 26391951936, 18531878400, 6059370240, 711244800, 0
OFFSET
0,8
FORMULA
T(n, k) = (-1)^n * n! * StirlingS1(n, k)*StirlingS1(n, n-k)/binomial(n, k).
EXAMPLE
Triangle begins as:
1;
0, 0;
0, 1, 0;
0, 12, 12, 0;
0, 216, 484, 216, 0;
0, 5760, 21000, 21000, 5760, 0;
0, 216000, 1117920, 1822500, 1117920, 216000, 0;
0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0;
MATHEMATICA
T[n_, k_]:= (-1)^n*n!*StirlingS1[n, k]StirlingS1[n, n-k]/Binomial[n, k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma) [(-1)^n*Factorial(n)*StirlingFirst(n, k)*StirlingFirst(n, n-k)/Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 03 2021
(Sage) flatten([[factorial(n)*stirling_number1(n, k)*stirling_number1(n, n-k)/binomial(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 03 2021
CROSSREFS
Cf. A048994.
Sequence in context: A254717 A195748 A038337 * A125509 A281251 A247511
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jan 28 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 03 2021
STATUS
approved