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 A156815 Triangle T(n, k) = n!*StirlingS2(n, k)/binomial(n, k), read by rows. 1
 1, 0, 1, 0, 1, 2, 0, 2, 6, 6, 0, 6, 28, 36, 24, 0, 24, 180, 300, 240, 120, 0, 120, 1488, 3240, 3120, 1800, 720, 0, 720, 15120, 43344, 50400, 33600, 15120, 5040, 0, 5040, 182880, 695520, 979776, 756000, 383040, 141120, 40320, 0, 40320, 2570400, 13068000, 22377600, 20018880, 11430720, 4656960, 1451520, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 99. LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = n!*StirlingS2(n, k)/binomial(n, k). From G. C. Greubel, Jun 10 2021: (Start) T(n, 1) = T(n, n) = n!. T(n, 2) = 2*A029767(n+1). T(n, n-1) = A180119(n). (End) EXAMPLE Triangle begins as: 1; 0, 1; 0, 1, 2; 0, 2, 6, 6; 0, 6, 28, 36, 24; 0, 24, 180, 300, 240, 120; 0, 120, 1488, 3240, 3120, 1800, 720; 0, 720, 15120, 43344, 50400, 33600, 15120, 5040; 0, 5040, 182880, 695520, 979776, 756000, 383040, 141120, 40320; MATHEMATICA T[n_, k_] = n!*StirlingS2[n, k]/Binomial[n, k]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten PROG (Magma) [Factorial(n)*StirlingSecond(n, k)/Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 10 2021 (Sage) flatten([[factorial(n)*stirling_number2(n, k)/binomial(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 10 2021 CROSSREFS Cf. A048993, A029767, A180119. Sequence in context: A291799 A295027 A225479 * A303439 A303345 A175802 Adjacent sequences: A156812 A156813 A156814 * A156816 A156817 A156818 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 16 2009 EXTENSIONS Edited by G. C. Greubel, Jun 10 2021 STATUS approved

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Last modified April 22 01:34 EDT 2024. Contains 371887 sequences. (Running on oeis4.)