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Search: id:A088925
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| A088925 |
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Square table, read by antidiagonals, of coefficients T(n,k) of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x-y) + xy*f(x,y)^3. |
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+0
4
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| 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 21, 10, 1, 1, 15, 55, 55, 15, 1, 1, 21, 120, 212, 120, 21, 1, 1, 28, 231, 644, 644, 231, 28, 1, 1, 36, 406, 1652, 2617, 1652, 406, 36, 1, 1, 45, 666, 3738, 8685, 8685, 3738, 666, 45, 1, 1, 55, 1035, 7680, 24735, 36345, 24735, 7680
(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 g.f. for A001764 satisfies: g(x) = 1 + x*g(x)^3.
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FORMULA
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T(n, k) = sum(i=0, k, C(n+k, 2i)*C(n+k-2i, k-i)*A001764(i) ), where A001764(i)=(3i)!/[i!(2i+1)! ] (from Michael Somos).
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EXAMPLE
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Rows begin:
{1, 1, 1, 1, 1, 1, 1, 1,..}
{1, 3, 6,10,15,21,28,..}
{1, 6,21,55,120,231,..}
{1,10,55,212,644,..}
{1,15,120,644,..}
{1,21,231,..}
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CROSSREFS
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Cf. A088926 (diagonal), A088927 (antidiagonal sums), A086617, A001764.
Sequence in context: A001263 A162747 A107105 this_sequence A100862 A098568 A131235
Adjacent sequences: A088922 A088923 A088924 this_sequence A088926 A088927 A088928
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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), Oct 23 2003
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