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

0,2

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.

Links

Table of n, a(n) for n=0..38.

Formula

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

Example

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 +...

Prog

(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)}

Crossrefs

Cf. A183037, A183038, A001511, A000123.

Sequence in context: A134016 A072297 A358908 * A120963 A370587 A200220

Adjacent sequences: A183033 A183034 A183035 * A183037 A183038 A183039

Keyword

nonn

Author

Paul D. Hanna, Dec 19 2010

Status

approved