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Search: id:A080242
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| A080242 |
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Table of coefficients of polynomials P(n,x) defined by the relation P(n,x) = (1+x)P(n-1,x) + (-x)^(n+1). |
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3
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| 1, 1, 1, 1, 1, 2, 2, 1, 3, 4, 2, 1, 1, 4, 7, 6, 3, 1, 5, 11, 13, 9, 3, 1, 1, 6, 16, 24, 22, 12, 4, 1, 7, 22, 40, 46, 34, 16, 4, 1, 1, 8, 29, 62, 86, 80, 50, 20, 5, 1, 9, 37, 91, 148, 166, 130, 70, 25, 5, 1, 1, 10, 46, 128, 239, 314, 296, 200, 95
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Values generate solutions to the recurrence a(n)=a(n-1) + k(k+1)a(n-2), a(0)=1, a(1)=k(k+1)+1 Values and sequences associated to this table are included in A072024
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FORMULA
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Rows are generated by P(n, x)=((x+1)^(n+2)-(-x)^(n+2))/(2x+1)
The polynomials P(n,-x), n > 0, satisfy a Riemann hypothesis: their zeros lie on the vertical line Re x = 1/2 in the complex plane. O.g.f.: (1+x*t+x^2*t)/((1+x*t)(1-t-x*t)) = 1+(1+x+x^2)*t+(1+2x+2x^2)*t^2+ ... . - Peter Bala (pbala(AT)toucansurf.com), Oct 24 2007
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EXAMPLE
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Rows are {1}, {1,1,1}, {1,2,2}, {1,3,4,2,1}, {1,4,7,6,3} This is the same as table A035317 with an extra 1 at the end of every second row.
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CROSSREFS
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Essentially the same as A059259 and A035317. Cf. A059260.
A001045 (row sums). Cf. A108561, A112555.
Adjacent sequences: A080239 A080240 A080241 this_sequence A080243 A080244 A080245
Sequence in context: A011020 A076019 A071453 this_sequence A035317 A103923 A061987
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 12 2003
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