A086636 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) = (3-sqrt(1-4x))/2 + xy*f(x,y)^3.

1, 1, 1, 1, 3, 3, 2, 6, 15, 12, 5, 13, 45, 84, 55, 14, 33, 120, 336, 495, 273, 42, 93, 330, 1092, 2475, 3003, 1428, 132, 280, 963, 3360, 9570, 18018, 18564, 7752, 429, 882, 2955, 10416, 33165, 81081, 129948, 116280, 43263, 1430, 2871, 9420, 33096, 110880

Offset

0,5

Comments

The main diagonal is A001764 ( C(3n,n)/(2n+1) ). First column is the Catalan sequence A000108, offset by 1. Antidiagonal sums also results in the Catalan sequence A000108.

Links

Table of n, a(n) for n=0..49.

Example

Rows begin:
{1},
{1,1},
{1,3,3},
{2,6,15,12},
{5,13,45,84,55},
{14,33,120,336,495,273},
{42,93,330,1092,2475,3003,1428},
{132,280,963,3360,9570,18018,18564,7752},
{429,882,2955,10416,33165,81081,129948,116280,43263}, ...

Crossrefs

Cf. A086637 (row sums), A001764, A000108 (Catalan).

Sequence in context: A106365 A200174 A266153 * A115055 A158468 A238278

Adjacent sequences: A086633 A086634 A086635 * A086637 A086638 A086639

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 24 2003

Status

approved