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A166553 Triangle read by rows: expansion of p(x,t) = -exp(x*t)(2*(1 - 2*exp(t)) - 2*exp(t))/(1 + exp(t)), with coefficient of x^n scaled by multiplication by  (n!*(n + 2)!/4). 0
1, 3, 3, 0, 24, 12, -30, 0, 180, 60, 0, -720, 0, 1440, 360, 2520, 0, -12600, 0, 12600, 2520, 0, 120960, 0, -201600, 0, 120960, 20160, -771120, 0, 3810240, 0, -3175200, 0, 1270080, 181440, 0, -61689600, 0, 101606400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

I think the rows are indexed by t = 0, 1, 2, ..., and in each row we expand the polynomial in powers of x. - N. J. A. Sloane, Dec 14 2010

Row sums are 1, 6, 36, 210, 1080, 5040, 60480, 1315440, 5443200, -558835200, 718502400,...

LINKS

Table of n, a(n) for n=0..39.

EXAMPLE

{1},

{3, 3},

{0, 24, 12},

{-30, 0, 180, 60},

{0, -720, 0, 1440, 360},

{2520, 0, -12600, 0, 12600, 2520},

{0, 120960, 0, -201600, 0, 120960, 20160},

{-771120, 0,3810240, 0, -3175200, 0, 1270080, 181440},

{0, -61689600, 0, 101606400, 0, -50803200, 0, 14515200, 1814400},

MATHEMATICA

p[t_] = -Exp[x*t](2*(1 - 2*Exp[t]) - 2*Exp[t])/(1 + Exp[t]);

a = Table[ CoefficientList[(n!*(n + 2)!/4)*SeriesCoefficient[

      Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}];

Flatten[a]

CROSSREFS

Sequence in context: A247889 A309012 A137259 * A285863 A111843 A119537

Adjacent sequences:  A166550 A166551 A166552 * A166554 A166555 A166556

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, Dec 12 2010

EXTENSIONS

I rewrote the definition. - N. J. A. Sloane, Dec 14 2010

STATUS

approved

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Last modified August 9 02:14 EDT 2020. Contains 336310 sequences. (Running on oeis4.)