%I A052129
%S A052129 1,1,2,12,576,1658880,16511297126400,1908360529573854283038720000,
%T A052129 29134719286683212541013468732221146917416153907200000000
%N A052129 a(n) = if n>0 then n*a(n-1)^2 else 1.
%D A052129 S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 
               2003, p. 446.
%D A052129 J. Guillera and J. Sondow, Double integrals and infinite products for 
               some classical constants via analytic continuations of Lerch's transcendent, 
               Ramanujan J. (to appear).
%D A052129 J. Sondow and P. Hadjicostas, The generalized-Euler-constant function 
               gamma(z) and a generalization of Somos's quadratic recurrence constant, 
               J. Math. Anal. Appl. (to appear).
%H A052129 J. Guillera and J. Sondow, <a href="http://arXiv.org/abs/math.NT/0506319">
               Double integrals and infinite products for some classical constants 
               via analytic continuations of Lerch's transcendent</a>
%H A052129 J. Sondow and P. Hadjicostas, <a href="http://arXiv.org/abs/math/0610499">
               The generalized-Euler-constant function gamma(z) and a generalization 
               of Somos's quadratic recurrence constant</a>
%H A052129 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SomossQuadraticRecurrenceConstant.html">Somos's Quadratic Recurrence 
               Constant</a>
%F A052129 a(n) ~ s^(2^n)/(n+2-1/n+4/n^2-21/n^3+138/n^4-1091/n^5+...) where s=1.661687949633... 
               (see A112302).
%e A052129 a(3) = 3*a(2)^2 = 3*(2*a(1)^2)^2 = 3*(2*(1*a(0)^2)^2)^2 = 3*(2*(1*1^2)^2)^2 
               = 3*(2*1)^2 = 3*4 = 12.
%o A052129 (PARI) {a(n)=if(n<0, 0, prod(i=0, n, (n-i+1)^2^i))} /* Michael Somos 
               Oct 22 2006 */
%Y A052129 Cf. A000142.
%Y A052129 A030450(n-1)=a(n)/n if n>0.
%Y A052129 Cf. A112302, A116603, A123851, A123852, A123853, A123854.
%Y A052129 Sequence in context: A145513 A002860 A108078 this_sequence A141770 A060055 
               A061149
%Y A052129 Adjacent sequences: A052126 A052127 A052128 this_sequence A052130 A052131 
               A052132
%K A052129 nonn,nice
%O A052129 0,3
%A A052129 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 12 2002