A086612 Triangle of coefficients, read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1+x) - x^2*(1+x)^2 + xy*f(x,y)^2.

1, 1, 1, -1, 2, 2, -2, -1, 6, 5, -1, -6, 0, 20, 14, 0, -5, -22, 10, 70, 42, 0, 2, -30, -80, 70, 252, 132, 0, 6, 6, -165, -280, 378, 924, 429, 0, 4, 52, -20, -840, -924, 1848, 3432, 1430, 0, 1, 48, 330, -406, -4032, -2772, 8580, 12870, 4862, 0, 0, 0, 440, 1750, -3528, -18480, -6864, 38610, 48620, 16796

Offset

0,5

Comments

The main diagonal gives the Catalan sequence A000108. Antidiagonal sums results in binomial {1,1}. Row sums give A086613.

Links

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

Example

Rows:
{1},
{1,1}
{-1,2,2},
{-2,-1,6,5},
{-1,-6,0,20,14},
{0,-5,-22,10,70,42},
{0,2,-30,-80,70,252,132},
{0,6,6,-165,-280,378,924,429},
{0,4,52,-20,-840,-924,1848,3432,1430},
{0,1,48,330,-406,-4032,-2772,8580,12870,4862}, ...

Crossrefs

Cf. A086613 (row sums), A086634.

Sequence in context: A255399 A181830 A352736 * A128207 A340740 A306707

Adjacent sequences: A086609 A086610 A086611 * A086613 A086614 A086615

Keyword

sign,tabl

Author

Paul D. Hanna, Jul 24 2003

Status

approved