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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

Table of n, a(n) for n=0..46.

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 January 18 10:53 EST 2019. Contains 319271 sequences. (Running on oeis4.)