A126965 a(n) = (2*n)!*(2*n-1)/(2^n*n!).

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

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.: sqrt(1-4*x)/(1-2*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*n-1)^2*a(n-1)=0. - R. J. Mathar, Jun 17 2016

Maple

seq( ((2*n)!*(2*n-1))/(2^n*n!), n=0..20); # G. C. Greubel, Jan 29 2020

Mathematica

Table[((2n)!(2n-1))/(2^n n!), {n, 0, 20}] (* Harvey P. Dale, Jan 16 2017 *)

Prog

(PARI) vector(21, n, my(m=n-1); ((2*m)!*(2*m-1))/(2^m*m!)) \\ G. C. Greubel, Mar 19 2017
(PARI) apply( {A126965(n)=(2*n)!*(2*n-1)/(2^n*n!)}, [0..20]) \\ M. F. Hasler, Feb 27 2020
(Magma) F:=Factorial; [(F(2*n)*(2*n-1))/(2^n*F(n)): n in [0..20]]; // G. C. Greubel, Jan 29 2020
(Sage) f=factorial; [(f(2*n)*(2*n-1))/(2^n*f(n)) for n in (0..20)] # G. C. Greubel, Jan 29 2020
(GAP) F:=Factorial;; List([0..20], n-> (F(2*n)*(2*n-1))/(2^n*F(n)) ); # G. C. Greubel, Jan 29 2020

Crossrefs

Cf. A001147.

Sequence in context: A136659 A231592 A335345 * A066222 A080254 A190916

Adjacent sequences: A126962 A126963 A126964 * A126966 A126967 A126968

Keyword

sign

Author

N. J. A. Sloane, Mar 21 2007

Status

approved