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A001880
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Coefficients of Bessel polynomials y_n (x).
(Formerly M4989 N2146)
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13
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1, 15, 210, 3150, 51975, 945945, 18918900, 413513100, 9820936125, 252070693875, 6957151150950, 205552193096250, 6474894082531875, 216659917377028125, 7675951358500425000, 287080580807915895000, 11303797869311688365625, 467445288360359818884375
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OFFSET
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4,2
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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E.g.f.: x*(1 + x/2)/(1 - 2*x)^(7/2); or, if shifted, (1+ 6x+ 3x^2/2!) / (1-2x)^(9/2).
a(n) = (2*n-4)!/(4!*(n-4)!*2^(n-4)).
(n-4)*a(n) = (n-2)*(2*n-5)*a(n-1) for n = 5, 6, .. , with a(4) = 1. - Johannes W. Meijer, May 24 2009
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MATHEMATICA
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nn = 25; t = Range[0, nn]! CoefficientList[Series[x (1 + x/2)/(1 - 2 x)^(7/2), {x, 0, nn}], x]; Drop[t, 1] (* T. D. Noe, Aug 10 2012 *)
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PROG
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(PARI) x='x+O('x^50); Vec(serlaplace(x*(1 + x/2)/(1 - 2*x)^(7/2))) \\ G. C. Greubel, Aug 13 2017
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CROSSREFS
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Equals the second right hand column of the triangles A094665 and A083061.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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