A086634 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)^3 + xy*f(x,y)^3.

1, 1, 1, -1, 3, 3, -3, 0, 15, 12, -3, -14, 15, 84, 55, -1, -27, -75, 168, 495, 273, 0, -9, -270, -336, 1485, 3003, 1428, 0, 47, -252, -2352, -825, 12012, 18564, 7752, 0, 93, 525, -4032, -18315, 6006, 92820, 116280, 43263, 0, 69, 1875, 2940, -49005, -129129, 129948, 697680, 735471, 246675

Offset

0,5

Comments

The main diagonal gives A001764 ( C(3n,n)/(2n+1) ). First column is given by g.f: (1+x) - x^2*(1+x)^3. Antidiagonal sums result in binomial {1,1,0,...}.

Links

Table of n, a(n) for n=0..54.

Example

Rows begin:
{1},
{1,1},
{-1,3,3},
{-3,0,15,12},
{-3,-14,15,84,55},
{-1,-27,-75,168,495,273},
{0,-9,-270,-336,1485,3003,1428},
{0,47,-252,-2352,-825,12012,18564,7752}, ...

Crossrefs

Cf. A086635 (row sums), A086632.

Sequence in context: A164884 A357073 A019801 * A066601 A110566 A126066

Adjacent sequences: A086631 A086632 A086633 * A086635 A086636 A086637

Keyword

sign,tabl

Author

Paul D. Hanna, Jul 25 2003

Status

approved