0,3

S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.

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).

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).

J. Guillera and J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent

J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant

Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant

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).

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.

(PARI) {a(n)=if(n<0, 0, prod(i=0, n, (n-i+1)^2^i))} /* Michael Somos Oct 22 2006 */

Cf. A000142.

A030450(n-1)=a(n)/n if n>0.

Cf. A112302, A116603, A123851, A123852, A123853, A123854.

Sequence in context: A145513 A002860 A108078 this_sequence A141770 A060055 A061149

Adjacent sequences: A052126 A052127 A052128 this_sequence A052130 A052131 A052132

nonn,nice

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 12 2002