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Search: id:A086612
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| A086612 |
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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. |
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+0
2
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| 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
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The main diagonal gives the Catalan sequence A000108. Antidiagonal sums results in binomial {1,1}. Row sums give A086613.
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EXAMPLE
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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}, ...
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CROSSREFS
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Cf. A086613 (row sums), A086634.
Sequence in context: A131308 A109978 A114293 this_sequence A128207 A037867 A122879
Adjacent sequences: A086609 A086610 A086611 this_sequence A086613 A086614 A086615
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003
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