login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 07 2009
STATUS
approved