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, 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

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