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A061702
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Triangle T(n,k) defined by Sum_{n >= 0,m >= 0} T(n,m)*x^n*y^m = y*(1 + 3*x - 4*x^2*y - 3*x^2*y^2 - 3*x^3*y^2 + 4*x^4*y^3)/((1 - y - 2*x*y - x*y^2 + x^3*y^3)*(1 - x*y)).
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2
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0, 1, 3, 1, 6, 5, 1, 9, 18, 6, 1, 12, 42, 44, 9, 1, 15, 75, 145, 95, 13, 1, 18, 117, 336, 420, 192, 20, 1, 21, 168, 644, 1225, 1085, 371, 31, 1, 24, 228, 1096, 2834, 3880, 2588, 696, 49, 1, 27, 297, 1719, 5652, 10656, 11097, 5823, 1278, 78, 1, 30, 375, 2540, 10165
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics I, Example 4.7.17.
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MATHEMATICA
| max = 11; f[x_, y_] := y*(1 + 3*x - 4*x^2*y - 3*x^2*y^2 - 3*x^3*y^2 + 4*x^4*y^3)/((1 - y - 2*x*y - x*y^2 + x^3*y^3)*(1 - x*y)); se = Series[f[x, y], {x, 0, max}, {y, 0, max}]; coes = CoefficientList[se, {x, y}] ; t[n_, k_] := coes[[k, n]]; Flatten[ Table[t[n, k], {n, 1, max}, {k, 1, n}]](* From Jean-François Alcover, Oct 24 2011 *)
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CROSSREFS
| Cf. A000183, row sums: A061703, third column: A000338, fourth column: A000561, fifth column: A000562, sixth column: A000563, seventh column: A000564, eighth column: A000565.
Sequence in context: A120394 A016575 A116666 * A112351 A143858 A109954
Adjacent sequences: A061699 A061700 A061701 * A061703 A061704 A061705
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 18 2001
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