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 A155742 Triangle T(n, k) = (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k), read by rows. 1
 1, 0, 0, 0, 1, 0, 0, 6, 6, 0, 0, 36, 121, 36, 0, 0, 240, 1750, 1750, 240, 0, 0, 1800, 23290, 50625, 23290, 1800, 0, 0, 15120, 308700, 1193640, 1193640, 308700, 15120, 0, 0, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 0, 0, 1451520, 59832864, 535810464, 1510458516, 1510458516, 535810464, 59832864, 1451520, 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*StirlingS1(n, k)*StirlingS1(n, n-k). Sum_{k=0..n} T(n, k) = A342111(n). - G. C. Greubel, Jun 05 2021 EXAMPLE Triangle begins as: 1; 0, 0; 0, 1, 0; 0, 6, 6, 0; 0, 36, 121, 36, 0; 0, 240, 1750, 1750, 240, 0; 0, 1800, 23290, 50625, 23290, 1800, 0; 0, 15120, 308700, 1193640, 1193640, 308700, 15120, 0; 0, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 0; MATHEMATICA T[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) A155742:= func< n, k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) >; [A155742(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 05 2021 (Sage) def A155742(n, k): return stirling_number1(n, k)*stirling_number1(n, n-k) flatten([[A155742(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 05 2021 CROSSREFS Cf. A048994, A342111 (row sums). Sequence in context: A283347 A334710 A283203 * A364406 A005597 A281056 Adjacent sequences: A155739 A155740 A155741 * A155743 A155744 A155745 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Jan 26 2009 EXTENSIONS Edited by G. C. Greubel, Jun 05 2021 STATUS approved

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Last modified July 18 13:57 EDT 2024. Contains 374378 sequences. (Running on oeis4.)