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A127945
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Hankel transform of central coefficients of (1+k*x-2x^2)^n, k arbitrary integer.
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3
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1, -4, -32, 512, 16384, -1048576, -134217728, 34359738368, 17592186044416, -18014398509481984, -36893488147419103232, 151115727451828646838272, 1237940039285380274899124224, -20282409603651670423947251286016
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OFFSET
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0,2
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COMMENTS
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Hankel transform of A098332. The Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-2)x) and its k-th binomial transforms, are given by a(n). In general, the Hankel transform of e.g.f. Bessel_I(0,2*sqrt(m)x) and its binomial transforms is 2^n*m^C(n+1,2).
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LINKS
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FORMULA
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a(n) = (cos(Pi*n/2) - sin(Pi*n/2))*4^n*2^C(n,2).
a(n) = 2^n*(-2)^C(n+1,2).
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MATHEMATICA
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Table[2^n*(-2)^Binomial[n+1, 2], {n, 0, 25}] (* G. C. Greubel, May 01 2018 *)
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PROG
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(PARI) for(n=0, 25, print1(2^n*(-2)^binomial(n+1, 2), ", ")) \\ G. C. Greubel, May 01 2018
(Magma) [2^n*(-2)^Binomial(n+1, 2): n in [0..25]]; // G. C. Greubel, May 01 2018
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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