0,8

Signed version of A046854.

Contribution from Paul Barry (pbarry(AT)wit.ie), May 21 2009: (Start)

Riordan array ((1-x)/(1+x^2),x/(1+x^2)).

This triangle is the coefficient triangle for the Hankel transforms of the family of generalized Catalan numbers

that satisfy a(n;r)=r*a(n-1;r)+sum{k=1..n-2, a(k)*a(n-1-k;r)}, a(0;r)=a(1;r)=1. The Hankel transform of

a(n;r) is h(n)=sum{k=0..n, T(n,k)*r^k} with g.f. (1-x)/(1-rx+x^2). These sequences include A086246, A000108, A002212. (End)

Number triangle T(n,k)=(-1)^C(n-k+1,2)*C(floor((n+k)/2),k). [From Paul Barry (pbarry(AT)wit.ie), May 21 2009]

Triangle begins:

1;

-1, 1;

-1, -1, 1;

1, -2, -1, 1;

1, 2, -3, -1, 1;

-1, 3, 3, -4, -1, 1;

-1, -3, 6, 4, -5, -1, 1;

1, -4, -6, 10, 5, -6, -1, 1;

1, 4, -10, -10, 15, 6, -7, -1, 1 ;...

Contribution from Paul Barry (pbarry(AT)wit.ie), May 21 2009: (Start)

Production matrix is

-1, 1,

-2, 0, 1,

-2, -1, 0, 1,

-4, 0, -1, 0, 1,

-6, -1, 0, -1, 0, 1,

-12, 0, -1, 0, -1, 0, 1,

-20, -2, 0, -1, 0, -1, 0, 1,

-40, 0, -2, 0, -1, 0, -1, 0, 1,

-70, -5, 0, -2, 0, -1, 0, -1, 0, 1 (End)

Cf. A066170 A046854.

Sequence in context: A144406 A096670 A130461 this_sequence A046854 A066170 A071773

Adjacent sequences: A130774 A130775 A130776 this_sequence A130778 A130779 A130780

sign,tabl

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 14 2007