A162580 G.f.: A(x) = exp( 2*Sum_{n>=1} 2^[A007814(n)^2] * x^n/n ), where A007814(n) = exponent of highest power of 2 dividing n.

1, 2, 4, 6, 16, 26, 44, 62, 240, 418, 756, 1094, 2544, 3994, 6556, 9118, 32352, 55586, 99492, 143398, 330000, 516602, 845900, 1175198, 3452112, 5729026, 9953556, 14178086, 31076592, 47975098, 77547580, 107120062, 298608832, 490097602

Offset: 0

Author

Paul D. Hanna, Jul 06 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 4*x^2 + 6*x^3 + 16*x^4 + 26*x^5 + 44*x^6 + ...
log(A(x))/2 = 2^0*x + 2^1*x^2 + 2^0*x^3/3 + 2^4*x^4/4 + 2^0*x^5/5 + 2^1*x^6/6 + 2^0*x^7/7 + 2^9*x^8/8 + ... + 2^[A007814(n)^2]*x^n/n + ...
		

Links

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

Crossrefs

Cf. A155200, A007814, A000123, A162581, A162582.

Programs

Mathematica

nmax = 500; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(IntegerExponent[k, 2]^2 + 1)*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=sum(m=1,n,2*2^(valuation(m,2)^2)*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}