

A126965


a(n) = (2*n)!*(2*n1)/(2^n*n!).


2



1, 1, 9, 75, 735, 8505, 114345, 1756755, 30405375, 585810225, 12439852425, 288735522075, 7273385294175, 197646339515625, 5763367260275625, 179518217255251875, 5948862302837829375, 208977775735174070625, 7757508341684492015625, 303429397707601987696875
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OFFSET

0,3


REFERENCES

V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250


FORMULA

E.g.f.: (14*x)^(1/2)/(12*x).
G.f.: x  1 + 9*x^2/(Q(0)9*x), where Q(k)= 1 + 9*x + 2*k*(1+6*x) + 4*x*k^2  x*(2*k+1)*(2*k+5)^2/Q(k+1); (continued fraction).  Sergei N. Gladkovskii, Apr 25 2013
a(n) = 1/sqrt(Pi) * Numerator(Gamma((2n+3)/2)  Gamma((2n+1)/2)), for n>=0. Denominators are 2^(n+1).  Richard R. Forberg, Feb 22 2015
+(2*n+3)*a(n) +(2*n1)^2*a(n1)=0.  R. J. Mathar, Jun 17 2016


MATHEMATICA

Table[((2n)!(2n1))/(2^n n!), {n, 0, 20}] (* Harvey P. Dale, Jan 16 2017 *)


PROG

(PARI) for(n=0, 25, print1(((2*n)!*(2*n1))/(2^n* n!), ", ")) \\ G. C. Greubel, Mar 19 2017


CROSSREFS

Cf. A001147.
Sequence in context: A223204 A136659 A231592 * A066222 A080254 A190916
Adjacent sequences: A126962 A126963 A126964 * A126966 A126967 A126968


KEYWORD

sign


AUTHOR

N. J. A. Sloane, Mar 21 2007


STATUS

approved



