A086632 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)^3 + xy*f(x,y)^3.

1, 1, 1, 0, 3, 3, -2, 3, 15, 12, -5, -5, 30, 84, 55, -9, -27, 0, 252, 495, 273, -14, -63, -180, 252, 1980, 3003, 1428, -20, -99, -612, -1008, 3630, 15015, 18564, 7752, -27, -99, -1200, -5544, -3465, 39039, 111384, 116280, 43263, -35, 0, -1320, -14280, -45045, 15015, 371280, 813960, 735471, 246675, -44, 286, 510

Offset

0,5

Comments

The main diagonal gives A001764 ( C(3n,n)/(2n+1) ). First column is given by g.f: 1/(1-x) - x^2/(1-x)^3. Antidiagonal sums result in all 1's.

Links

Table of n, a(n) for n=0..57.

Example

Rows begin:
{1},
{1,1},
{0,3,3},
{-2,3,15,12},
{-5,-5,30,84,55},
{-9,-27,0,252,495,273},
{-14,-63,-180,252,1980,3003,1428},
{-20,-99,-612,-1008,3630,15015,18564,7752}, ...

Crossrefs

Cf. A086633 (row sums), A086634.

Sequence in context: A123676 A326814 A122775 * A038699 A249803 A350833

Adjacent sequences: A086629 A086630 A086631 * A086633 A086634 A086635

Keyword

sign,tabl

Author

Paul D. Hanna, Jul 24 2003

Status

approved