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 A157047 A triangle of infinite sum coefficients with: Limit[Log[1-x],x->0]=-x: p(x,y)=1+n!*x^(n - 1)*Sum[x^k/(k*Binomial[n + k, k]), {k, 1, Infinity}]; such that Log[1-x]->-x. 0
 2, 1, 1, 1, -1, 2, 1, 3, -7, 6, 1, -12, 40, -46, 24, 1, 60, -260, 430, -326, 120, 1, -360, 1920, -4140, 4536, -2556, 720, 1, 2520, -15960, 42420, -60732, 49644, -22212, 5040, 1, -20160, 147840, -467040, 825216, -883008, 574848, -212976, 40320, 1, 181440 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are:1+n!; {2, 2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881,...}. LINKS FORMULA Limit[Log[1-x],x->0]=-x: p(x,y)=1+n!*x^(n - 1)*Sum[x^k/(k*Binomial[n + k, k]), {k, 1, Infinity}]; such that Log[1-x]->-x. EXAMPLE {2}, {1, 1}, {1, -1, 2}, {1, 3, -7, 6}, {1, -12, 40, -46, 24}, {1, 60, -260, 430, -326, 120}, {1, -360, 1920, -4140, 4536, -2556, 720}, {1, 2520, -15960, 42420, -60732, 49644, -22212, 5040}, {1, -20160, 147840, -467040, 825216, -883008, 574848, -212976, 40320}, {1, 181440, -1512000, 5533920, -11630304, 15374016, -13120704, 7090416, -2239344, 362880}, {1, -1814400, 16934400, -70459200, 171642240, -270043200, 284947200, -202111200, 93297600, -25659360, 3628800} MATHEMATICA Clear[p, x, n, m]; p[x_, n_] = n!*x^(n - 1)*Sum[x^k/(k*Binomial[n + k, k]), {k, 1, Infinity}] Table[ExpandAll[1 + p[x, n] /. Log[1 - x] -> -x], {n, 0, 10}] Table[CoefficientList[ExpandAll[1 + p[x, n] /. Log[1 - x] -> - x], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A029434 A156281 A002217 * A059342 A062831 A037828 Adjacent sequences:  A157044 A157045 A157046 * A157048 A157049 A157050 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 22 2009 STATUS approved

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Last modified October 15 00:02 EDT 2019. Contains 328025 sequences. (Running on oeis4.)