

A086612


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)^2 + xy*f(x,y)^2.


1



1, 1, 1, 1, 2, 2, 2, 1, 6, 5, 1, 6, 0, 20, 14, 0, 5, 22, 10, 70, 42, 0, 2, 30, 80, 70, 252, 132, 0, 6, 6, 165, 280, 378, 924, 429, 0, 4, 52, 20, 840, 924, 1848, 3432, 1430, 0, 1, 48, 330, 406, 4032, 2772, 8580, 12870, 4862, 0, 0, 0, 440, 1750, 3528, 18480, 6864, 38610, 48620, 16796
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OFFSET

0,5


COMMENTS

The main diagonal gives the Catalan sequence A000108. Antidiagonal sums results in binomial {1,1}. Row sums give A086613.


LINKS

Table of n, a(n) for n=0..65.


EXAMPLE

Rows:
{1},
{1,1}
{1,2,2},
{2,1,6,5},
{1,6,0,20,14},
{0,5,22,10,70,42},
{0,2,30,80,70,252,132},
{0,6,6,165,280,378,924,429},
{0,4,52,20,840,924,1848,3432,1430},
{0,1,48,330,406,4032,2772,8580,12870,4862}, ...


CROSSREFS

Cf. A086613 (row sums), A086634.
Sequence in context: A285183 A255399 A181830 * A128207 A180958 A295854
Adjacent sequences: A086609 A086610 A086611 * A086613 A086614 A086615


KEYWORD

sign,tabl


AUTHOR

Paul D. Hanna, Jul 24 2003


STATUS

approved



