A101485 a(n) = (4n)! / ( 4^n * (2n)! ).

1, 3, 105, 10395, 2027025, 654729075, 316234143225, 213458046676875, 191898783962510625, 221643095476699771875, 319830986772877770815625, 563862029680583509947946875, 1192568192774434123539907640625, 2980227913743310874726229193921875

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

sin(arcsin(2x)/2) = x + 3x^3/3! + 105x^5/5! + 10395x^7/7! + ...

E.g.f.: cosh(x^2/2). - Paul Barry, Sep 28 2010

a(n) = 4^n*Gamma(2*n+1/2) / Gamma(1/2). - Peter Luschny, Jul 05 2011

Hypergeom. recurrence: a(n) -(4*n-1)*(4*n-3)*a(n-1)=0. - R. J. Mathar, Sep 21 2012

Sum_{n>=0} 1/a(n) = 1 + (1/2) * sqrt(e*Pi/2) * erf(1/sqrt(2)) - (1/2) * sqrt(Pi/(2*e)) * erfi(1/sqrt(2)), where erf is the error function and erfi is the imaginary error function. - Amiram Eldar, Jan 08 2023

Maple

seq(4^n*pochhammer(1/2, 2*n), n=0..12); # Peter Luschny, Jul 05 2011

Mathematica

f[n_] := 4^n*Pochhammer[1/2, 2 n]; Array[f, 13, 0] (* Robert G. Wilson v, Jul 05 2011 *)

Prog

(PARI) a(n)=(4*n)!/(2*n)!>>(2*n) \\ Charles R Greathouse IV, Jul 06 2011

Crossrefs

Bisection of A001147. Odd part of A009120.

Sequence in context: A334776 A346086 A271049 * A226236 A074072 A352656

Adjacent sequences: A101482 A101483 A101484 * A101486 A101487 A101488

Keyword

nonn,easy

Author

Ralf Stephan, Jan 21 2005

Status

approved