A201824 - OEIS

%I #19 Jul 19 2024 12:04:22

%S 1,1,3,20,330,15504,2324784,1198774720,2214919483920,

%T 14955617450039552,372282884729800002816,34307640086657221926620160,

%U 11737947382912650038702322439680,14950677150224267346380689021913026560,71100479076279984636914230616119201295462400

%N G.f.: Sum_{n>=0} log( 1/sqrt(1-2^n*x) )^n / n!.

%F a(n) = binomial(2^(n-1) + n - 1, n).

%F a(n) = A006127(n-1)*A060690(n-1)/n for n>0. - _Hugo Pfoertner_, Jul 19 2024

%e G.f.: A(x) = 1 + x + 3*x^2 + 20*x^3 + 330*x^4 + 15504*x^5 +...

%e where

%e 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! +...

%o (PARI) {a(n)=binomial(2^(n-1)+n-1, n)}

%o (PARI) {a(n)=polcoef(sum(m=0,n+1,log(1/sqrt(1-2^m*x +x^2*O(x^n)))^m/m!),n)}

%Y Cf. A002416, A006127, A060690.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 05 2011