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

0,3

Links

Table of n, a(n) for n=0..14.

Formula

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

a(n) = A006127(n-1)*A060690(n-1)/n for n>0. - Hugo Pfoertner, Jul 19 2024

Example

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! +...

Prog

(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)}

Crossrefs

Cf. A002416, A006127, A060690.

Sequence in context: A130531 A240777 A163138 * A203519 A003150 A326869

Adjacent sequences: A201821 A201822 A201823 * A201825 A201826 A201827

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2011

Status

approved