A086626 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)^3.

1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 6, 9, 6, 1, 1, 10, 24, 24, 10, 1, 1, 15, 57, 84, 57, 15, 1, 1, 21, 120, 249, 249, 120, 21, 1, 1, 28, 228, 654, 907, 654, 228, 28, 1, 1, 36, 399, 1554, 2880, 2880, 1554, 399, 36, 1, 1, 45, 654, 3384, 8178, 10821, 8178, 3384, 654, 45, 1, 1, 55, 1017, 6831, 21156, 35949, 35949, 21156, 6831, 1017, 55, 1

Offset

0,8

Links

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

Example

Rows begin:
1,_1,__1,___1,____1,_____1,_____1,______1, ...
1,_1,__3,___6,___10,____15,____21,_____28, ...
1,_3,__9,__24,___57,___120,___228,____399, ...
1,_6,_24,__84,__249,___654,__1554,___3384, ...
1,10,_57,_249,__907,__2880,__8178,__21156, ...
1,15,120,_654,_2880,_10821,_35949,_107952, ...
1,21,228,1554,_8178,_35949,137832,_473331, ...
1,28,399,3384,21156,107952,473331,1840560, ...

Mathematica

m = 12; f[_, _] = 0;
Do[f[x_, y_] = (1 - x y)/((1 - x)(1 - y)) + x y f[x, y]^3 + O[x]^m, {m}];
T = CoefficientList[# + O[y]^m, y]& /@ CoefficientList[f[x, y], x];
Table[T[[n-k+1, k]], {n, 1, m}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 15 2019 *)

Crossrefs

Cf. A086627 (diagonal), A086628 (antidiagonal sums).

Sequence in context: A015109 A319699 A157636 * A244500 A300695 A296186

Adjacent sequences: A086623 A086624 A086625 * A086627 A086628 A086629

Keyword

nonn,tabl

Author

Paul D. Hanna, Jul 24 2003

Status

approved