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

%I A101485 #22 Jan 08 2023 02:44:16
%S A101485 1,3,105,10395,2027025,654729075,316234143225,213458046676875,
%T A101485 191898783962510625,221643095476699771875,319830986772877770815625,
%U A101485 563862029680583509947946875,1192568192774434123539907640625,2980227913743310874726229193921875
%N A101485 a(n) = (4n)! / ( 4^n * (2n)! ).
%F A101485 sin(arcsin(2x)/2) = x + 3x^3/3! + 105x^5/5! + 10395x^7/7! + ...
%F A101485 E.g.f.: cosh(x^2/2). - _Paul Barry_, Sep 28 2010
%F A101485 a(n) = 4^n*Gamma(2*n+1/2) / Gamma(1/2). - _Peter Luschny_, Jul 05 2011
%F A101485 Hypergeom. recurrence: a(n) -(4*n-1)*(4*n-3)*a(n-1)=0. - _R. J. Mathar_, Sep 21 2012
%F A101485 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
%p A101485 seq(4^n*pochhammer(1/2,2*n), n=0..12); # _Peter Luschny_, Jul 05 2011
%t A101485 f[n_] := 4^n*Pochhammer[1/2, 2 n]; Array[f, 13, 0] (* _Robert G. Wilson v_, Jul 05 2011 *)
%o A101485 (PARI) a(n)=(4*n)!/(2*n)!>>(2*n) \\ _Charles R Greathouse IV_, Jul 06 2011
%Y A101485 Bisection of A001147. Odd part of A009120.
%K A101485 nonn,easy
%O A101485 0,2
%A A101485 _Ralf Stephan_, Jan 21 2005