# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a183036 Showing 1-1 of 1 %I A183036 #10 Mar 30 2012 18:37:23 %S A183036 1,2,6,10,24,38,74,110,200,290,486,682,1096,1510,2314,3118,4650,6182, %T A183036 8946,11710,16616,21522,29886,38250,52328,66406,89394,112382,149496, %U A183036 186610,245086,303562,394814,486066,625686,765306,977112,1188918,1504954 %N 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. %C A183036 Compare to B(x), the g.f. of the binary partitions (A000123): %C A183036 B(x) = exp( Sum_{n>=1} 2^A001511(n)*x^n/n ) = (1-x)^(-1)*Product_{n>=0} 1/(1 - x^(2^n)). %C A183036 2^A001511(n) exactly divides 2n. %F A183036 G.f. satisfies: A(x) = (1-x^2)/(1-x)^2 * A(x^2)^2/A(x^4). %e A183036 G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 24*x^4 + 38*x^5 + 74*x^6 +... %e A183036 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 +... %o A183036 (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)} %Y A183036 Cf. A183037, A183038, A001511, A000123. %K A183036 nonn %O A183036 0,2 %A A183036 _Paul D. Hanna_, Dec 19 2010 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE