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.

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

Offset: 0

Author

Paul D. Hanna, Jul 07 2009

Keywords

• nonn

Examples

			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 + ...
		

Links

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

Crossrefs

Cf. A006519, A000123.

Programs

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 *)

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)}