0,2

A cubic analog of the asymptotic expansion A116603 of Somos's quadratic recurrence sequence A052129. Numerators are A123853.

Equals 2^A004134(n); also the denominators in expansion of (1-x)^{-1/4}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2006

All terms are powers of 2. Log[2,a(n)] = A004134(n) = 3n - A000120(n) = {0, 2, 5, 7, 11, 13, 16, 18, 23, 25, 28, 30, 34, 36, 39, 41, 47, 49, 52, 54, 58, 60, 63, 65, 70, 72, 75, 77, 81, 83, 86, 88, 95, 97, 100, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2006

Is this the same sequence as A088802? - njas, Mar 21, 2007

Almost certainly this is the same as A088802. - Michael Somos Aug 23 2007

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

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. 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) = 2^A004134[n]. a(n) = 2^(3n - A000120(n)). - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 27 2006

A123851(n) ~ c^(3^n)*n^(- 1/2)/(1 + 3/4n - 15/32n^2 + 113/128n^3 - 5397/2048n^4 + ...) where c = 1.1563626843322... is the cubic recurrence constant A123852.

f:=proc(t, x) exp(sum(ln(1+m*x)/t^m, m=1..infinity)); end; for j from 0 to 29 do denom(coeff(series(f(3, x), x=0, 30), x, j)); od;

Cf. A052129, A112302, A116603, A123851, A123852, A123853.

Cf. A004134, A004130, A000120.

Sequence in context: A033430 A088658 A088802 this_sequence A112850 A113154 A083299

Adjacent sequences: A123851 A123852 A123853 this_sequence A123855 A123856 A123857

frac,nonn

Petros Hadjicostas and Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 15 2006