A086610 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/(1-x) - x^2/(1-x)^2 + xy*f(x,y)^2.

1, 1, 1, 0, 2, 2, -1, 1, 6, 5, -2, -2, 6, 20, 14, -3, -6, -4, 30, 70, 42, -4, -10, -24, 0, 140, 252, 132, -5, -13, -48, -95, 70, 630, 924, 429, -6, -14, -66, -240, -350, 588, 2772, 3432, 1430, -7, -12, -66, -370, -1176, -1134, 3696, 12012, 12870, 4862, -8, -6, -36, -380, -2100, -5544, -2772, 20592, 51480, 48620, 16796

Offset

0,5

Comments

The main diagonal gives the Catalan sequence A000108. Antidiagonal sums results in all 1's. Row sums give A086611.

Links

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

Example

Rows:
{1},
{1,1},
{0,2,2},
{-1,1,6,5},
{-2,-2,6,20,14},
{-3,-6,-4,30,70,42},
{-4,-10,-24,0,140,252,132},
{-5,-13,-48,-95,70,630,924,429},
{-6,-14,-66,-240,-350,588,2772,3432,1430},
{-7,-12,-66,-370,-1176,-1134,3696,12012,12870,4862}, ...

Crossrefs

Cf. A086611 (row sums), A086632.

Sequence in context: A136587 A136247 A370207 * A141760 A114626 A221916

Adjacent sequences: A086607 A086608 A086609 * A086611 A086612 A086613

Keyword

sign,tabl

Author

Paul D. Hanna, Jul 24 2003

Status

approved