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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. 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, 1 (list; table; graph; refs; listen; history; text; internal format)
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..78.

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

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)