A110152 G.f.: A(x) = Product_{n>=1} 1/(1 - 2^n*x^n)^(2/2^n).

1, 2, 6, 14, 36, 78, 192, 406, 942, 2018, 4512, 9450, 21178, 43950, 95532, 200398, 431356, 892518, 1917572, 3950614, 8410230, 17398466, 36648980, 75326754, 159199004, 326471706, 683028924, 1404145162, 2930071798, 5993625942

Offset: 0

Author

Paul D. Hanna, Jul 14 2005

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 6*x^2 + 14*x^3 + 36*x^4 + 78*x^5 +...
where
A(x) = 1/((1-2*x) * (1-4*x^2)^(1/2) * (1-8*x^3)^(1/4) * (1-16*x^4)^(1/8) *...).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A110153, A110154, A110155, A110156.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[1/(1 - 2^k*x^k)^(2/2^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 18 2020 *)

PARI

a(n)=polcoeff(prod(k=1,n,1/(1-2^k*x^k+x*O(x^n))^(2/2^k)),n)

PARI

A090879(n) = sumdiv(n,d, d*2^(n-d))
a(n)=local(A);A=exp(sum(k=1,n,2*A090879(k)*x^k/k)+x*O(x^n));polcoeff(A,n)
for(n=0,30,print1(a(n),", ")) \\ Paul D. Hanna, Jan 05 2014

Formula

G.f.: exp( Sum_{n>=1} 2*A090879(n)*x^n/n ), where A090879(n) = Sum_{d|n} d*2^(n-d). - Paul D. Hanna, Jan 05 2014