A180687 G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x/(1-x))^n/n!.

1, 2, 8, 70, 2008, 209018, 76000040, 94978699326, 410326957417208, 6211396910763188786, 334321755307017208207432, 64835518006826024523658441206, 45812575197824183928260946747286552

Offset: 0

Author

Paul D. Hanna, Sep 16 2010

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 70*x^4 + 2008*x^5 +...
A(x) = Sum_{n>=0} log(1 + 2^n*x + 2^n*x^2 + 2^n*x^3 + 2^n*x^4 +...)^n/n!.
A(x) = 1 + log(1+2x/(1-x)) + log(1+4x/(1-x))^2/2! + log(1+8x/(1-x))^3/3! +...
		

Crossrefs

Cf. variants: A159602, A060690.

Programs

PARI

{a(n)=polcoeff(sum(m=0, n, log(1+2^m*x/(1-x+x*O(x^n)))^m/m!), n)}

Formula

a(n) = Sum_{k=0..n} binomial(2^k, k) * binomial(n-1, n-k) for n >= 0. - Paul D. Hanna, Apr 04 2023