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Search: id:A008482
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| A008482 |
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Coefficients in expansion of (x-1)(1+x)^(n-1), n>0. |
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+0
5
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| 0, -1, 1, -1, 0, 1, -1, -1, 1, 1, -1, -2, 0, 2, 1, -1, -3, -2, 2, 3, 1, -1, -4, -5, 0, 5, 4, 1, -1, -5, -9, -5, 5, 9, 5, 1, -1, -6, -14, -14, 0, 14, 14, 6, 1, -1, -7, -20, -28, -14, 14, 28, 20, 7, 1, -1, -8, -27, -48, -42, 0, 42, 48, 27, 8, 1, -1, -9, -35, -75, -90, -42, 42
(list; table; graph; listen)
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OFFSET
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0,12
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COMMENT
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Apart from initial term, same as A112467. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 07 2006
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REFERENCES
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A. A. Kirillov, Variations on the triangular theme, Amer. Math. Soc. Transl., (2), Vol. 169, 1995, pp. 43-73, see p. 71.
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LINKS
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I. Gessel and S. Ree, Lattice paths and Faber polynomials.
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FORMULA
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T(n, k)=T(n-1, k-1)+T(n-1, k); T(0, 0)=0, T(1, 0)=-11, T(1, 1)=1.
T(n, k)=C(n, k-1)-C(n, k) where C = binomial coefficient A007318.
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EXAMPLE
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0; 1 -1; 1 0 -1; 1 1 -1 -1; 1 2 0 -2 -1; 1 3 2 -2 -3 -1; ...
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PROGRAM
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(PARI) T(n, k)=if(n<1, 0, polcoeff((x-1)*(1+x)^(n-1), k))
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CROSSREFS
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Skew analogue of Pascal's triangle A007318, central column gives Catalan numbers A000108, essentially same as A037012, except rows are read from left to right (A037012 = - this sequence).
The positive half of this triangle is A008315 - Michael Somos . Cf. A037012.
Sequence in context: A079627 A061398 A080232 this_sequence A037012 A112467 A112466
Adjacent sequences: A008479 A008480 A008481 this_sequence A008483 A008484 A008485
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KEYWORD
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sign,easy,tabl
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AUTHOR
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njas
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