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 A217553 G.f.: exp( Sum_{n>=1} 4^A001511(n) * x^n/n ), where 2^A001511(n) is the highest power of 2 that divides 2*n. 3
 1, 4, 16, 44, 128, 308, 752, 1628, 3584, 7268, 14864, 28556, 55296, 102036, 189168, 337084, 603136, 1044676, 1814288, 3064556, 5188352, 8578548, 14205936, 23041308, 37420800, 59680548, 95265552, 149620812, 235161216, 364301652, 564627952, 863725948, 1321756672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare g.f. to the g.f. of binary partitions (A000123): exp( Sum_{n>=1} 2^A001511(n) * x^n/n ). LINKS Table of n, a(n) for n=0..32. FORMULA Self-convolution of A162581. EXAMPLE G.f.: A(x) = 1 + 4*x + 16*x^2 + 44*x^3 + 128*x^4 + 308*x^5 + 752*x^6 +... where log(A(x)) = 4^1*x + 4^2*x^2/2 + 4^1*x^3/3 + 4^4*x^4/4 + 4^1*x^5/5 + 4^2*x^6/6 + 4^1*x^7/7 + 4^4*x^8/8 + 4^1*x^9/9 + 4^2*x^10/10 + 4^1*x^11/11 + 4^4*x^12/12 +...+ 4^A001511(n)*x^n/n +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, 4^valuation(2*m, 2)*x^m/m)+x*O(x^n)), n)} for(n=0, 31, print1(a(n), ", ")) CROSSREFS Cf. A162581, A180591, A001511. Sequence in context: A054498 A360278 A293629 * A225379 A359073 A134139 Adjacent sequences: A217550 A217551 A217552 * A217554 A217555 A217556 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 30 2012 STATUS approved

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Last modified September 25 11:40 EDT 2023. Contains 365644 sequences. (Running on oeis4.)