A086623 Symmetric square table of coefficients, read by antidiagonals, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1-xy)/[(1-x)(1-y)] + xy*f(x,y)^2.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 8, 8, 4, 1, 1, 5, 14, 19, 14, 5, 1, 1, 6, 22, 40, 40, 22, 6, 1, 1, 7, 32, 76, 100, 76, 32, 7, 1, 1, 8, 44, 132, 222, 222, 132, 44, 8, 1, 1, 9, 58, 213, 448, 570, 448, 213, 58, 9, 1, 1, 10, 74, 324, 834, 1316, 1316, 834, 324, 74, 10, 1

Offset

0,8

Comments

The first row and column of 1's together form: (1-xy)/[(1-x)(1-y)], while the remaining square table (excluding the first row and column) give the coefficients of f(x,y)^2.

Links

Table of n, a(n) for n=0..77.

Example

Rows begin:
  1,1, 1,  1,   1,   1,    1,    1,     1, ...
  1,1, 2,  3,   4,   5,    6,    7,     8, ...
  1,2, 4,  8,  14,  22,   32,   44,    58, ...
  1,3, 8, 19,  40,  76,  132,  213,   324, ...
  1,4,14, 40, 100, 222,  448,  834,  1450, ...
  1,5,22, 76, 222, 570, 1316, 2782,  5458, ...
  1,6,32,132, 448,1316, 3442, 8180, 17928, ...
  1,7,44,213, 834,2782, 8180,21685, 52694, ...
  1,8,58,324,1450,5458,17928,52694,141112, ...

Crossrefs

Cf. A086624 (diagonal), A086625 (antidiagonal sums).

Sequence in context: A072405 A146565 A115594 * A248736 A292508 A237597

Adjacent sequences: A086620 A086621 A086622 * A086624 A086625 A086626

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 24 2003

Status

approved