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Search: id:A132460
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| A132460 |
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Triangle read by rows of the initial [n/2]+1 coefficients of 1/C(x)^n, where C(x) is the g.f. of the Catalan sequence (A000108). |
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+0
2
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| 1, 1, 1, -2, 1, -3, 1, -4, 2, 1, -5, 5, 1, -6, 9, -2, 1, -7, 14, -7, 1, -8, 20, -16, 2, 1, -9, 27, -30, 9, 1, -10, 35, -50, 25, -2, 1, -11, 44, -77, 55, -11, 1, -12, 54, -112, 105, -36, 2, 1, -13, 65, -156, 182, -91, 13, 1, -14, 77, -210, 294, -196, 49, -2
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Essentially equals a signed version of A034807, the triangle of Lucas polynomials. The initial n coefficients of 1/C(x)^n consist of row n followed by [(n-1)/2] zeros for n>0.
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FORMULA
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T(n,k) = (-1)^k*( C(n-k,k) + C(n-k-1,k-1) ) for n>=0, 0<=k<=[n/2].
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EXAMPLE
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Triangle begins:
1;
1;
1, -2;
1, -3;
1, -4, 2;
1, -5, 5;
1, -6, 9, -2;
1, -7, 14, -7;
1, -8, 20, -16, 2;
1, -9, 27, -30, 9;
1, -10, 35, -50, 25, -2;
1, -11, 44, -77, 55, -11;
1, -12, 54, -112, 105, -36, 2;
1, -13, 65, -156, 182, -91, 13;
1, -14, 77, -210, 294, -196, 49, -2; ...
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PROGRAM
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(PARI) {T(n, k)=if(k>n\2, 0, (-1)^k*(binomial(n-k, k)+binomial(n-k-1, k-1)))}
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CROSSREFS
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Cf. A132461 (row squared sums); A034807 (Lucas polynomials); A000108.
Sequence in context: A113398 A056538 A120385 this_sequence A067734 A067004 A117920
Adjacent sequences: A132457 A132458 A132459 this_sequence A132461 A132462 A132463
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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), Aug 21 2007
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