A038121 E.g.f.: (1 + 15*x + (45/2)*x^2 + (5/2)*x^3)/(1 - 2*x)^(13/2).
1, 28, 630, 13860, 315315, 7567560, 192972780, 5237832600, 151242416325, 4638100767300, 150738274937250, 5179915266025500, 187771928393424375, 7164221267933730000, 287080580807915895000, 12057384393932467590000
Offset: 0
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Selden Crary, Richard Diehl Martinez, Michael Saunders, The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters, arXiv:1707.00705 [stat.ME], 2017, Table 1.
Programs
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Magma
[Factorial(2*n+6)/ (720*Factorial(n)*2^n): n in [0..20]]; // Vincenzo Librandi, Nov 22 2011
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Mathematica
Table[(2n+6)!/(6!*n!*2^n),{n,0,20}] (* Vincenzo Librandi, Nov 22 2011 *) -
PARI
x='x+O('x^50); Vec(serlaplace((1+15*x+45/2*x^2+5/2*x^3)/(1-2*x)^(13/2))) \\ G. C. Greubel, Aug 13 2017
Formula
a(n) = (2n+6)! / (6!*n!*2^n).
n*a(n) - (n+3)*(2*n+5)*a(n-1) = 0. - R. J. Mathar, Oct 31 2015