A201824 G.f.: Sum_{n>=0} log( 1/sqrt(1-2^n*x) )^n / n!.
1, 1, 3, 20, 330, 15504, 2324784, 1198774720, 2214919483920, 14955617450039552, 372282884729800002816, 34307640086657221926620160, 11737947382912650038702322439680, 14950677150224267346380689021913026560, 71100479076279984636914230616119201295462400
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 20*x^3 + 330*x^4 + 15504*x^5 +... where A(x) = 1 + log(1/sqrt(1-2*x)) + log(1/sqrt(1-4*x))^2/2! + log(1/sqrt(1-8*x))^3/3! + log(1/sqrt(1-16*x))^4/4! +...
Programs
-
PARI
{a(n)=binomial(2^(n-1)+n-1, n)} -
PARI
{a(n)=polcoef(sum(m=0,n+1,log(1/sqrt(1-2^m*x +x^2*O(x^n)))^m/m!),n)}
Formula
a(n) = binomial(2^(n-1) + n - 1, n).