A137384 Triangle: No(x, n) = (2*n/x)*No(x, n - 1) + (-n/(n - 2))*No( x, n - 2) + Ceiling[(2*(n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x; weighted by 2*x^(n + 1).

2, 2, 8, 0, 2, 48, 0, 6, 384, 0, 32, 0, -10, 3840, 0, 240, 0, -110, 46080, 0, 2304, 0, -1368, 0, 21, 645120, 0, 26880, 0, -19488, 0, 448, 10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32, 185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152, 3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Example

{2},
{2},
{8, 0, 2},
{48, 0, 6},
{384, 0, 32, 0, -10},
{3840, 0, 240, 0, -110},
{46080, 0, 2304, 0, -1368, 0, 21},
{645120, 0, 26880, 0, -19488,0, 448},
{10321920, 0, 368640, 0, -314880, 0, 8992, 0, -32},
{185794560, 0, 5806080, 0, -5702400, 0, 186912, 0, -1152},
{3715891200, 0, 103219200, 0, -114508800, 0, 4131840, 0, -34280, 0, 46}
...

Mathematica

No[x, -1] = 0;
No[x, 0] = 1/x;
No[x, 1] = 1/x^2;
No[x, 2] = (x^2 + 4)/x^3;
No[x_, n_] := No[x, n] = (2*n/x)*No[ x, n - 1] + (-n/(n - 2))*No[x, n - 2] + Ceiling[(2*( n - 1)/((n - 2)))*Sin[(n - 1)*Pi/2]]/x;
Table[ExpandAll[2*x^(n + 1)*No[x, n]], {n, 0, 10}];
a = Table[CoefficientList[2*x^(n + 1)*No[x, n], x], {n, 0, 10}];
Flatten[a]

Crossrefs

Sequence in context: A248237 A139523 A359057 * A051148 A102645 A366324

Adjacent sequences: A137381 A137382 A137383 * A137385 A137386 A137387

Keyword

uned,tabf,sign,less

Author

Roger L. Bagula, Apr 09 2008

Status

approved