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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

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

Adjacent sequences: A155822 A155823 A155824 * A155826 A155827 A155828

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Jan 28 2009

EXTENSIONS

Edited by G. C. Greubel, Jun 03 2021

STATUS

approved

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Last modified January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)