A137660 Triangular sequence of coefficients from the expansion of p(x,t)=Tan(x*t)/Tan(t).

0, 1, 0, -4, 0, 4, 0, -64, 0, -320, 0, 384, 0, -7680, 0, -26880, 0, -161280, 0, 195840, 0, -3096576, 0, -10321920, 0, -43352064, 0, -263208960, 0, 319979520, 0, -3096576000, 0, -10218700800, 0, -40874803200, 0, -173717913600, 0, -1055932416000, 0, 1283840409600

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..42.

Formula

p(x,t)=Tan(x*t)/Tan(t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=(n+1)!*n!*Coefficients(p(x,n)) for even n.

Example

{0, 1},
{0, -4, 0, 4},
{0, -64, 0, -320, 0, 384},
{0, -7680, 0, -26880, 0, -161280, 0, 195840},
{0, -3096576, 0, -10321920, 0, -43352064, 0, -263208960, 0, 319979520},
{0, -3096576000, 0, -10218700800, 0, -40874803200, 0, -173717913600, 0, -1055932416000, 0, 1283840409600}

Mathematica

p[t_] = Tan[x*t]/Tan[t]; Table[ ExpandAll[(n+1)!*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10, 2}]; a = Table[ CoefficientList[(n+1)!*n!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]

Crossrefs

Sequence in context: A035622 A112919 A019201 * A123583 A236112 A226787

Adjacent sequences: A137657 A137658 A137659 * A137661 A137662 A137663

Keyword

tabf,sign

Author

Roger L. Bagula, Apr 27 2008

Status

approved