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A162589 G.f.: A(x) = exp( Sum_{n>=1} 2^n*A006519(n) * x^n/n ), where A006519(n) = highest power of 2 dividing n. 1
1, 2, 6, 12, 38, 76, 188, 376, 1094, 2188, 5236, 10472, 26076, 52152, 118840, 237680, 612678, 1225356, 2804420, 5608840, 13279604, 26559208, 59074504, 118149008, 277925148, 555850296, 1228260104, 2456520208, 5552652792, 11105305584 (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 + 2*x + 6*x^2 + 12*x^3 + 38*x^4 + 76*x^5 + 188*x^6 + ...

log(A(x)) = 2*x + 8*x^2/2 + 8*x^3/3 + 64*x^4/4 + 32*x^5/5 + 128*x^6/6 + 128*x^7/7 + ...

MATHEMATICA

nmax = 150; a[n_]:= SeriesCoefficient[Series[Exp[Sum[2^(k + 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=sum(m=1, n, 2^(m+valuation(m, 2))*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

CROSSREFS

Cf. A162588, A006519, A000123.

Sequence in context: A189854 A189565 A074442 * A225957 A123045 A280171

Adjacent sequences:  A162586 A162587 A162588 * A162590 A162591 A162592

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 07 2009

STATUS

approved

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)