A183036 G.f.: exp( Sum_{n>=1} A001511(n)*2^A001511(n)*x^n/n ) where A001511(n) equals the 2-adic valuation of 2n.

1, 2, 6, 10, 24, 38, 74, 110, 200, 290, 486, 682, 1096, 1510, 2314, 3118, 4650, 6182, 8946, 11710, 16616, 21522, 29886, 38250, 52328, 66406, 89394, 112382, 149496, 186610, 245086, 303562, 394814, 486066, 625686, 765306, 977112, 1188918, 1504954

Offset: 0

Author

Paul D. Hanna, Dec 19 2010

Keywords

• nonn

Comments

Compare to B(x), the g.f. of the binary partitions (A000123):

B(x) = exp( Sum_{n>=1} 2^A001511(n)*x^n/n ) = (1-x)^(-1)*Product_{n>=0} 1/(1 - x^(2^n)).

2^A001511(n) exactly divides 2n.

Examples

			G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 24*x^4 + 38*x^5 + 74*x^6 +...
log(A(x)) = 2*x + 8*x^2/2 + 2*x^3/3 + 24*x^4/4 + 2*x^5/5 + 8*x^6/6 + 2*x^7/7 + 64*x^8/8 + 2*x^9/9 + 8*x^10/10 +...+ A183037(n)*x^n/n +...
		

Crossrefs

Cf. A183037, A183038, A001511, A000123.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n,valuation(2*m,2)*2^valuation(2*m,2)*x^m/m)+x*O(x^n)),n)}

Formula

G.f. satisfies: A(x) = (1-x^2)/(1-x)^2 * A(x^2)^2/A(x^4).