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Search: id:A037012
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| A037012 |
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Coefficients in expansion of (1-x)(1+x)^(n-1), n>0. |
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+0
6
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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, -90
(list; table; graph; listen)
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OFFSET
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0,12
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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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FORMULA
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T(n, k)=T(n-1, k-1)+T(n-1, k); T(0, 0)=0, T(1, 0)=1, T(1, 1)=-1.
T(n, k)=C(n, k)-C(n, k-1) where C = binomial coefficient A007318.
G.f.: (1-y) / (1-x-xy). - R. Stephan, Jan 23 2005
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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((1-x)*(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 A008482, except rows are read from left to right (A037012 = - this sequence).
Apart from initial term, same as A080232.
Sequence in context: A061398 A080232 A008482 this_sequence A112467 A112466 A166348
Adjacent sequences: A037009 A037010 A037011 this_sequence A037013 A037014 A037015
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KEYWORD
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sign,easy,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Michael Somos.
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