This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A162581 G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^2 * x^n/n ), where A006519(n) = highest power of 2 dividing n. 4
 1, 2, 6, 10, 26, 42, 86, 130, 258, 386, 694, 1002, 1754, 2506, 4134, 5762, 9346, 12930, 20198, 27466, 42330, 57194, 85750, 114306, 169602, 224898, 326934, 428970, 618138, 807306, 1144390, 1481474, 2084610, 2687746, 3732422, 4777098, 6591386 (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 + 10*x^3 + 26*x^4 + 42*x^5 + 86*x^6 + ... log(A(x))/2 = 2^0*x + 2^2*x^2 + 2^0*x^3/3 + 2^4*x^4/4 + 2^0*x^5/5 + 2^2*x^6/6 + 2^0*x^7/7 + 2^6*x^8/8 + ... + A006519(n)^2*x^n/n + ... MATHEMATICA nmax = 200; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(2*IntegerExponent[k, 2] + 1)*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*(2^valuation(m, 2))^2*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)} CROSSREFS Cf. A162580, A162582, A006519, A000123. Sequence in context: A055237 A057434 A217381 * A061547 A218791 A320429 Adjacent sequences:  A162578 A162579 A162580 * A162582 A162583 A162584 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 06 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 03:41 EST 2019. Contains 329968 sequences. (Running on oeis4.)