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 A174544 A mirrored symmetrical triangle of the Stirling numbers of the second kind. 0
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 15, 15, 1, 1, 1, 1, 31, 90, 31, 1, 1, 1, 1, 63, 301, 301, 63, 1, 1, 1, 1, 127, 966, 1701, 966, 127, 1, 1, 1, 1, 255, 3025, 7770, 7770, 3025, 255, 1, 1, 1, 1, 511, 9330, 34105, 42525, 34105, 9330, 511, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Row Sums are: 1, 2, 3, 4, 11, 34, 156, 732, 3891, 22104, 130421,... LINKS FORMULA T(n,0) = 1. T(n,k) = A008277(n,k) if 1<=k<=n/2. T(n,k) = T(n,n-k). EXAMPLE 1; 1, 1; 1, 1, 1; 1, 1, 1, 1; 1, 1, 7, 1, 1; 1, 1, 15, 15, 1, 1; 1, 1, 31, 90, 31, 1, 1; 1, 1, 63, 301, 301, 63, 1, 1; 1, 1, 127, 966, 1701, 966, 127, 1, 1; 1, 1, 255, 3025, 7770, 7770, 3025, 255, 1, 1; 1, 1, 511, 9330, 34105, 42525, 34105, 9330, 511, 1, 1; MATHEMATICA t[n_, m_, q_] = If[m == 0 || m == n, 1, If[Floor[n/2] >= m, StirlingS2[n, m]*q^ m, StirlingS2[n, n - m]*q^(n - m)]]; Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}] CROSSREFS Sequence in context: A285483 A284097 A091258 * A168423 A336844 A072101 Adjacent sequences:  A174541 A174542 A174543 * A174545 A174546 A174547 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Mar 22 2010 EXTENSIONS Formula and NAME cleaned up by R. J. Mathar, Aug 28 2013 STATUS approved

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Last modified August 5 14:57 EDT 2021. Contains 346469 sequences. (Running on oeis4.)