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Search: id:A086636
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| A086636 |
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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) = (3-sqrt(1-4x))/2 + xy*f(x,y)^3. |
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+0
2
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| 1, 1, 1, 1, 3, 3, 2, 6, 15, 12, 5, 13, 45, 84, 55, 14, 33, 120, 336, 495, 273, 42, 93, 330, 1092, 2475, 3003, 1428, 132, 280, 963, 3360, 9570, 18018, 18564, 7752, 429, 882, 2955, 10416, 33165, 81081, 129948, 116280, 43263, 1430, 2871, 9420, 33096, 110880
(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 is A001764 ( C(3n,n)/(2n+1) ). First column is the Catalan sequence A000108, offset by 1. Antidiagonal sums also results in the Catalan sequence A000108.
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EXAMPLE
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Rows begin:
{1},
{1,1},
{1,3,3},
{2,6,15,12},
{5,13,45,84,55},
{14,33,120,336,495,273},
{42,93,330,1092,2475,3003,1428},
{132,280,963,3360,9570,18018,18564,7752},
{429,882,2955,10416,33165,81081,129948,116280,43263}, ...
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CROSSREFS
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Cf. A086637 (row sums), A001764, A000108 (Catalan).
Sequence in context: A083343 A110898 A106365 this_sequence A115055 A100052 A128504
Adjacent sequences: A086633 A086634 A086635 this_sequence A086637 A086638 A086639
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003
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