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 A176153 Triangle read by rows:t(n,m)=Sum[StirlingS1[n, n - k]*Binomial[n, k], {k, 0, m}] 0
 1, 1, 1, 1, -1, -1, 1, -8, -2, -2, 1, -23, 43, 19, 19, 1, -49, 301, -199, -79, -79, 1, -89, 1186, -3314, 796, 76, 76, 1, -146, 3529, -22196, 34644, -2400, 2640, 2640, 1, -223, 8793, -100967, 372863, -362529, 3375, -36945, -36945, 1, -323, 19333, -361691 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are: {2, -1, -11, 59, -104, -1268, 18712, -152577, 650050, 5365931,...}. LINKS FORMULA t(n,m)=Sum[StirlingS1[n, n - k]*Binomial[n, k], {k, 0, m}] EXAMPLE {1}, {1, 1}, {1, -1, -1}, {1, -8, -2, -2}, {1, -23, 43, 19, 19}, {1, -49, 301, -199, -79, -79}, {1, -89, 1186, -3314, 796, 76, 76}, {1, -146, 3529, -22196, 34644, -2400, 2640, 2640}, {1, -223, 8793, -100967, 372863, -362529, 3375, -36945, -36945}, {1, -323, 19333, -361691, 2466883, -6010901, 3911515, -33509, 329371, 329371}, {1, -449, 38701, -1095299, 12192031, -55677869, 96294931, -44429069, 1766851, -1861949, -1861949} MATHEMATICA t[n_, m_] := Sum[StirlingS1[n, n - k]*Binomial[n, k], {k, 0, m}]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A177428 A130617 A010150 * A136711 A037920 A138997 Adjacent sequences:  A176150 A176151 A176152 * A176154 A176155 A176156 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 10 2010 STATUS approved

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