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 A156811 Triangle read by rows: t(n,m)=If[BernoulliB[n - m] == 0, 0, Binomial[n, m]*BernoulliB[n - m]^(-m)]. 1
 1, 1, 1, 1, -4, 1, 0, 18, 12, 1, 1, 0, 216, -32, 1, 0, -150, 0, 2160, 80, 1, 1, 0, 13500, 0, 19440, -192, 1, 0, 294, 0, -945000, 0, 163296, 448, 1, 1, 0, 49392, 0, 56700000, 0, 1306368, -1024, 1, 0, -270, 0, 6223392, 0, -3061800000, 0, 10077696, 2304, 1, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, -2, 31, 186, 2091, 32750, -780961, 58054738, -3045496877, 153819074262,...}. Steve Roman gives this function as one for the Stirling 2nd numbers,but the results doesn't turn out right in Mathematica. REFERENCES Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 99. LINKS FORMULA t(n,m)=If[BernoulliB[n - m] == 0, 0, Binomial[n, m]*BernoulliB[n - m]^(-m)]. EXAMPLE {1}, {1, 1}, {1, -4, 1}, {0, 18, 12, 1}, {1, 0, 216, -32, 1}, {0, -150, 0, 2160, 80, 1}, {1, 0, 13500, 0, 19440, -192, 1}, {0, 294, 0, -945000, 0, 163296, 448, 1}, {1, 0, 49392, 0, 56700000, 0, 1306368, -1024, 1}, {0, -270, 0, 6223392, 0, -3061800000, 0, 10077696, 2304, 1}, {1, 0, 40500, 0, 653456160, 0, 153090000000, 0, 75582720, -5120, 1} MATHEMATICA Clear[t, n, m]; t[n_, m_] = If[ BernoulliB[n - m] == 0, 0, Binomial[n, m]*BernoulliB[n - m]^(-m)]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A007789 A081114 A069018 * A246609 A130636 A299354 Adjacent sequences:  A156808 A156809 A156810 * A156812 A156813 A156814 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 16 2009 STATUS approved

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Last modified April 22 09:30 EDT 2021. Contains 343174 sequences. (Running on oeis4.)