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 A137369 Triangle read by rows: expansion of p(t) = (1 + t)^x/(1 + (1 + t)^n) with weight factor 2^(n+1)*n!. 0
 1, -1, 2, 4, -12, 4, 30, 88, -60, 8, -1344, 224, 752, -224, 16, -16920, -31232, 0, 4320, -720, 32, 2977920, -430848, -371264, -10560, 19840, -2112, 64, 53267760, 104934912, -5789056, -3084928, -101920, 78848, -5824, 128, -24148131840, 1882583040, 1867684864, -54942720, -20344576, -645120, 283136 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..43. Eric Weisstein's World of Mathematics, Boole Polynomial. EXAMPLE {1}, {-1, 2}, {4, -12, 4}, {30, 88, -60, 8}, {-1344, 224, 752, -224, 16}, {-16920, -31232,0, 4320, -720, 32}, {2977920, -430848, -371264, -10560, 19840, -2112, 64}, {53267760, 104934912, -5789056, -3084928, -101920, 78848, -5824, 128}, MATHEMATICA p[t_] = (1 + t)^x/(1 + (1 + t)^n) Table[ ExpandAll[2^(n + 1)*n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[2^(n + 1)*n!*SeriesCoefficient[Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Sequence in context: A075554 A365000 A294103 * A334766 A336847 A338118 Adjacent sequences: A137366 A137367 A137368 * A137370 A137371 A137372 KEYWORD uned,tabl,sign AUTHOR Roger L. Bagula, Apr 09 2008 STATUS approved

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Last modified June 14 04:49 EDT 2024. Contains 373393 sequences. (Running on oeis4.)