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 A156593 Triangle: q=2; m=1; t(n,k) = If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m) = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. 0
 1, 1, 1, 1, -2, 1, 1, 2, 2, 1, 1, 2, -2, 2, 1, 1, -6, 6, 6, -6, 1, 1, -14, -42, -42, -42, -14, 1, 1, 26, 182, -546, -546, 182, 26, 1, 1, 178, -2314, 16198, -48594, 16198, -2314, 178, 1, 1, 90, -8010, -104130, 728910, 728910, -104130, -8010, 90, 1, 1, -2382, 107190 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS EXAMPLE {1}, {1, 1}, {1, -2, 1}, {1, 2, 2, 1}, {1, 2, -2, 2, 1}, {1, -6, 6, 6, -6, 1}, {1, -14, -42, -42, -42, -14, 1}, {1, 26, 182, -546, -546, 182, 26, 1}, {1, 178, -2314, 16198, -48594, 16198, -2314, 178, 1}, {1, 90, -8010, -104130, 728910, 728910, -104130, -8010, 90, 1}, {1, -2382, 107190, 9539910, 124018830, 289377270, 124018830, 9539910, 107190, -2382, 1} MATHEMATICA t[n_, m_] = If[m == 0, n!, Product[Sum[(-1)^i* StirlingS2[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b[n_, k_, m_] = f[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]; Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}] CROSSREFS Sequence in context: A348042 A143209 A163994 * A206498 A184848 A184720 Adjacent sequences:  A156590 A156591 A156592 * A156594 A156595 A156596 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 10 2009 STATUS approved

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Last modified May 20 09:27 EDT 2022. Contains 353871 sequences. (Running on oeis4.)