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A162588 G.f.: A(x) = exp( 2*Sum_{n>=1} 2^n/A006519(n) * x^n/n ), where A006519(n) = highest power of 2 dividing n. 2
1, 4, 10, 24, 52, 112, 240, 512, 1060, 2192, 4552, 9440, 19408, 39872, 81984, 168448, 342632, 696736, 1421200, 2897856, 5891872, 11976064, 24361856, 49543168, 100329952, 203147136, 411939264, 835168512, 1690383744, 3420860928 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

EXAMPLE

G.f.: A(x) = 1 + 4*x + 10*x^2 + 24*x^3 + 52*x^4 + 112*x^5 + 240*x^6 + ...

log(A(x))/2 = 2*x + 2*x^2/2 + 8*x^3/3 + 4*x^4/4 + 32*x^5/5 + 32*x^6/6 + 128*x^7/7 + ...

MATHEMATICA

nmax = 150; a[n_]:= SeriesCoefficient[Series[Exp[Sum[2^(k + 1 - IntegerExponent[k, 2])*q^k/k, {k, 1, nmax}]], {q, 0, nmax}], n]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jul 04 2018 *)

PROG

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

CROSSREFS

Cf. A006519, A000123.

Sequence in context: A274582 A052365 A107659 * A280541 A080615 A173729

Adjacent sequences:  A162585 A162586 A162587 * A162589 A162590 A162591

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 07 2009

STATUS

approved

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Last modified March 21 18:59 EDT 2019. Contains 321382 sequences. (Running on oeis4.)