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

0,2

Links

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

Example

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 + ...

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 *)

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. A155200, A007814, A000123, A162581, A162582.

Sequence in context: A078148 A076075 A030157 * A098426 A365639 A279480

Adjacent sequences: A162577 A162578 A162579 * A162581 A162582 A162583

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2009

Status

approved