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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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2
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1, -4, -32, 512, 16384, -1048576, -134217728, 34359738368, 17592186044416, -18014398509481984, -36893488147419103232, 151115727451828646838272, 1237940039285380274899124224, -20282409603651670423947251286016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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).
Unsigned version is A036442 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 11 2008]
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FORMULA
| a(n)=(cos(pi*n/2)-sin(pi*n/2))*4^n*2^C(n,2)=2^n*(-2)^C(n+1,2)
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CROSSREFS
| Sequence in context: A140179 A118990 A036442 * A186339 A086899 A013041
Adjacent sequences: A127942 A127943 A127944 * A127946 A127947 A127948
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 08 2007
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