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).

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

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