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A138364
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Coefficients of I_1(2z) where I_1 is the hyperbolic Bessel function of order 1.
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6
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0, 1, 0, 3, 0, 10, 0, 35, 0, 126, 0, 462, 0, 1716, 0, 6435, 0, 24310, 0, 92378, 0, 352716, 0, 1352078, 0, 5200300, 0, 20058300, 0, 77558760, 0, 300540195, 0, 1166803110, 0, 4537567650, 0, 17672631900, 0, 68923264410, 0, 269128937220, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| An aerated version of A001700, which is the main entry for this sequence.
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REFERENCES
| Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials and random matrices", preprint, 2008.
Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Ch. 49, Hemisphere Publishing Corp., 1999.
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LINKS
| Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices.
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FORMULA
| a(n)=binomial(n,(n+1)/2) for n odd, 0 otherwise. egf is I_1(2z).
a(n) = (1/(2*Pi))*integral(x=-2..2, x^n*x/sqrt((2+x)*(2-x))). [Peter Luschny, Sep 12 2011]
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EXAMPLE
| a(5)=10 since the coefficient of z^5 in I_1(2z) is binomial(5,3)=10.
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CROSSREFS
| Cf. A001700, A126869.
Sequence in context: A167352 A094472 A028850 * A095364 A094052 A161678
Adjacent sequences: A138361 A138362 A138363 * A138365 A138366 A138367
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KEYWORD
| easy,nonn
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AUTHOR
| Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 16 2008
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