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 A155999 Triangle T(n, k) = (-1)^n*StirlingS2(n, k)*StirlingS2(n, n-k), read by rows. 1
 1, 0, 0, 0, 1, 0, 0, -3, -3, 0, 0, 6, 49, 6, 0, 0, -10, -375, -375, -10, 0, 0, 15, 2015, 8100, 2015, 15, 0, 0, -21, -8820, -105350, -105350, -8820, -21, 0, 0, 28, 33782, 1014300, 2893401, 1014300, 33782, 28, 0, 0, -36, -117810, -8004150, -54009270, -54009270, -8004150, -117810, -36, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are: {1, 0, 1, -6, 61, -770, 12160, -228382, 4989621, -124262532, 3475892685, ...}. LINKS G. C. Greubel, Rows n = 0..100 of the triangle, flattened FORMULA T(n, k) = (-1)^n*StirlingS2(n, k)*StirlingS2(n, n-k) EXAMPLE Triangle begins as: 1; 0, 0; 0, 1, 0; 0, -3, -3, 0; 0, 6, 49, 6, 0; 0, -10, -375, -375, -10, 0; 0, 15, 2015, 8100, 2015, 15, 0; 0, -21, -8820, -105350, -105350, -8820, -21, 0; 0, 28, 33782, 1014300, 2893401, 1014300, 33782, 28, 0; 0, -36, -117810, -8004150, -54009270, -54009270, -8004150, -117810, -36, 0; MATHEMATICA T[n_, k_]:= (-1)^n*StirlingS2[n, k]*StirlingS2[n, n-k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten PROG (Sage) def A155999(n, k): return (-1)^n*stirling_number2(n, k)*stirling_number2(n, n-k) flatten([[A155999(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 27 2021 (Magma) A155999:= func< n, k | (-1)^n*StirlingSecond(n, k)*StirlingSecond(n, n-k) >; [A155999(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 27 2021 (PARI) T(n, k) = (-1)^n*stirling(n, k, 2)*stirling(n, n-k, 2); matrix(10, 10, n, k, n--; k--; if (n>=k, T(n, k))) \\ Michel Marcus, Feb 27 2021 CROSSREFS Cf. A048993. Sequence in context: A300175 A129533 A360849 * A338034 A299904 A221768 Adjacent sequences: A155996 A155997 A155998 * A156000 A156001 A156002 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Feb 01 2009 EXTENSIONS Edited by G. C. Greubel, Feb 27 2021 STATUS approved

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)