A120616 Generalized Riordan array (1/sqrt(1+4x^2),(1-sqrt(1+4x^2))/(2x)).

1, 0, -1, -2, 0, 1, 0, 3, 0, -1, 6, 0, -4, 0, 1, 0, -10, 0, 5, 0, -1, -20, 0, 15, 0, -6, 0, 1, 0, 35, 0, -21, 0, 7, 0, -1, 70, 0, -56, 0, 28, 0, -8, 0, 1, 0, -126, 0, 84, 0, -36, 0, 9, 0, -1, -252, 0, 210, 0, -120, 0, 45, 0, -10, 0, 1

Offset

0,4

Comments

Product by A007318 is A104505.

Links

Table of n, a(n) for n=0..65.

Formula

Number triangle T(n,k)=C(n,(n+k)/2)(-1)^((n+k)/2)(1+(-1)^(n+k))/2.

abs(T(n,k)) = A108044(n,k).

Example

Triangle begins
.1,
.0, -1,
.-2, 0, 1,
.0, 3, 0, -1,
.6, 0, -4, 0, 1,
.0, -10, 0, 5, 0, -1,
.-20, 0, 15, 0, -6, 0, 1,
.0, 35, 0, -21, 0, 7, 0, -1,
.70, 0, -56, 0, 28, 0, -8, 0, 1,
.0, -126, 0, 84, 0, -36, 0, 9, 0, -1,
.-252, 0, 210, 0, -120, 0, 45, 0, -10, 0, 1

Crossrefs

Sequence in context: A320602 A134511 A112554 * A108044 A104477 A224928

Adjacent sequences: A120613 A120614 A120615 * A120617 A120618 A120619

Keyword

easy,sign,tabl

Author

Paul Barry, Jun 17 2006

Status

approved