0,12

Row sums are A000007. Diagonal sums are -F(n-2). Inverse is A112468. T(2n,n)=0.

(-1,1)-Pascal triangle . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 07 2006

Apart from initial term, same as A008482. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 07 2006

Dominique Foata, Guo-Niu Han, THE DOUBLOON POLYNOMIAL TRIANGLE, http://www-irma.u-strasbg.fr/~foata/paper/pub112.html [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 16 2009]

Number triangle T(n, k)=C(n, n-k)-2*C(n-1, n-k-1);

Sum_{k, 0<=k<=n} T(n, k)*x^k = (x-1)*(x+1)^(n-1) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 03 2005

t(j,n)=If[n == 0, 1, ((2*n - j + 1)/n)*Binomial[j - 2, n - 1]]. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 16 2009]

Triangle starts

1;

-1,1;

-1,0,1;

-1,-1,1,1;

-1,-2,0,2,1;

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

-1,-4,-5,0,5,4,1;

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 16 2009: (Start)

{1},

{1, 1},

{1, 0, 1},

{1, -1, 1, 1},

{1, -2, 0, 2, 1},

{1, -3, -2, 2, 3, 1},

{1, -4, -5, 0, 5, 4, 1},

{1, -5, -9, -5, 5, 9, 5, 1},

{1, -6, -14, -14, 0, 14, 14, 6, 1},

{1, -7, -20, -28, -14, 14, 28, 20, 7, 1},

{1, -8, -27, -48, -42, 0, 42, 48, 27, 8, 1},

{1, -9, -35, -75, -90, -42, 42, 90, 75, 35, 9, 1} (End)

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 16 2009: (Start)

d[n_, j_] = If[n == 0, 1, ((2*n - j + 1)/n)*Binomial[j - 2, n - 1]];

Table[Table[d[n, j], {n, 0, j - 1}], {j, 1, 12}];

Flatten[%] (End)

Cf. A008482, A037012, A112466.

Cf. A080232, A112466, A112467 [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 16 2009]

Sequence in context: A080232 A008482 A037012 this_sequence A112466 A166348 A127543

Adjacent sequences: A112464 A112465 A112466 this_sequence A112468 A112469 A112470

easy,sign,tabl

Paul Barry (pbarry(AT)wit.ie), Sep 06 2005