A106334 Decimal expansion of the function F(x) evaluated at the constant x that satisfies: F(x) - x*F'(x) = 0, where F(x) = Sum_{n>=0} x^(n*(n+1)/2).

1, 9, 8, 7, 3, 6, 9, 7, 2, 1, 1, 8, 4, 6, 8, 4, 1, 4, 5, 2, 6, 9, 2, 8, 9, 7, 8, 3, 3, 4, 4, 4, 1, 2, 6, 1, 8, 3, 4, 2, 7, 1, 7, 7, 2, 9, 8, 5, 5, 4, 5, 7, 4, 7, 0, 3, 5, 6, 2, 2, 3, 1, 0, 3, 8, 2, 6, 9, 5, 8, 9, 3, 8, 8, 6, 6, 2, 5, 5, 4, 7, 7, 6, 2, 0, 9, 7, 6, 2, 9, 9, 6, 3, 3, 6, 5, 7, 2, 7, 4, 6, 8, 1, 3, 5

Offset

1,2

Comments

Constant A106333 divided by this constant equals constant A106335, the radius of convergence of the g.f. of A106336.

Links

Table of n, a(n) for n=1..105.

Example

F(x)=1.9873697211846841452692897833444126183427177298554574703562231
where F(x) = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + ...
at x = 0.6411803884299545796456448886283011... (A106333).

Mathematica

digits = 105; x0 = x /. FindRoot[ Sum[(1 - n*(n+1)/2)*x^(n*(n+1)/2), {n, 0, digits}], {x, 1/2}, WorkingPrecision -> digits+5]; f[x_] := EllipticTheta[2, 0, Sqrt[x]]/(2*x^(1/8)); f[x0] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 05 2013 *)

Prog

(PARI) A106333=solve(x=.6, .7, sum(n=0, 100, (1-n*(n+1)/2)*x^(n*(n+1)/2))); A106334=sum(n=0, 100, A106333^(n*(n+1)/2))

Crossrefs

Cf. A106333, A106335, A106332, A106336.

Sequence in context: A278828 A334448 A011116 * A089739 A199264 A022965

Adjacent sequences: A106331 A106332 A106333 * A106335 A106336 A106337

Keyword

cons,nonn

Author

Paul D. Hanna, Apr 29 2005

Status

approved