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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 May 20 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)