cp's OEIS Frontend

A139825 Decimal expansion of constant c = Sum_{n>=0} C(3/2^n, n).

%I A139825 #2 Mar 30 2012 18:37:10
%S A139825 2,4,4,7,8,6,2,6,0,5,7,5,1,5,7,7,0,3,5,0,3,2,2,7,0,0,5,6,4,9,1,2,5,1,
%T A139825 5,3,5,1,6,3,2,6,2,9,6,4,9,4,1,4,3,1,4,6,3,3,8,8,3,8,1,6,7,8,1,8,9,7,
%U A139825 9,3,0,5,7,8,0,8,5,5,0,0,4,7,9,7,7,6,0,1,6,6,3,3,8,1,9,8,5,7,2,6,5,8,5,9,9
%N A139825 Decimal expansion of constant c = Sum_{n>=0} C(3/2^n, n).
%F A139825 c = Sum_{n>=0} log(1 + 1/2^n)^n*3^n/n! .
%e A139825 c = 2.44786260575157703503227005649125153516326296494143146338838167...
%e A139825 c = 1 + 3/2 - 3/32 + 65/1024 - 16965/524288 + 4112925/268435456 +...
%e A139825 c = 1 + log(3/2)*3 + log(5/4)^2*3^2/2! + log(9/8)^3*3^3/3! +...
%e A139825 The formulas for this constant illustrate the identity:
%e A139825 Sum_{n>=0} log(1 + q^n*x)^n*y^n/n! = Sum_{n>=0} binomial(q^n*y, n)*x^n.
%o A139825 (PARI) a(n)=local(c=sum(m=0,n+2,log(1+1/2^m)^m*3^m/m!));floor(c*10^n)%10
%Y A139825 Cf. A139823, A139824.
%K A139825 cons,nonn
%O A139825 1,1
%A A139825 _Paul D. Hanna_, May 01 2008