A137562 Triangular sequence of coefficients from the expansion of p(x,t)=Cos(x*t)/Cos(t).

1, 0, 1, 0, -1, 0, 5, 0, -6, 0, 1, 0, 61, 0, -75, 0, 15, 0, -1, 0, 1385, 0, -1708, 0, 350, 0, -28, 0, 1, 0, 50521, 0, -62325, 0, 12810, 0, -1050, 0, 45, 0, -1

Offset

1,7

Comments

Row sums are: {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};

Links

Table of n, a(n) for n=1..41.

Formula

p(x,t)=Cos(x*t)/Cos(t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=n!*Coefficients(p(x,n)).

Example

{1},
{0},
{1, 0, -1},
{0},
{5, 0, -6, 0, 1},
{0},
{61, 0, -75, 0, 15, 0, -1},
{0},
{1385, 0, -1708, 0, 350, 0, -28, 0, 1},
{0},
{50521, 0, -62325,0, 12810, 0, -1050, 0, 45, 0, -1}

Mathematica

p[t_] = Cos[x*t]/Cos[t]; Table[ ExpandAll[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] Flatten[{{1}, {0}, {1, 0, -1}, {0}, {5, 0, -6, 0, 1}, {0}, {61, 0, -75, 0, 15, 0, -1}, {0}, {1385, 0, -1708, 0, 350, 0, -28, 0, 1}, {0}, {50521, 0, -62325, 0, 12810, 0, -1050, 0, 45, 0, -1}}]

Crossrefs

Sequence in context: A055953 A165051 A154855 * A021668 A004552 A130415

Adjacent sequences: A137559 A137560 A137561 * A137563 A137564 A137565

Keyword

tabf,sign

Author

Roger L. Bagula, Apr 27 2008

Status

approved