A162582 G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^n * x^n/n ), where A006519(n) = highest power of 2 dividing n.

1, 2, 6, 10, 146, 282, 826, 1370, 4204986, 8408602, 25223066, 42037530, 615687706, 1189337882, 3483938586, 5778539290, 2305851850537847066, 4611703695297154842, 13835111074334385946, 23058518453371617050

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 146*x^4 + 282*x^5 + 826*x^6 + ...
log(A(x))/2 = 2^0*x + 2^2*x^2 + 2^0*x^3/3 + 2^8*x^4/4 + 2^0*x^5/5 + 2^6*x^6/6 + 2^0*x^7/7 + 2^24*x^8/8 + ... + A006519(n)^n*x^n/n + ...

Mathematica

nmax = 200; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(k*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))^m*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

Crossrefs

Cf. A162580, A162581, A155200, A006519, A000123.

Sequence in context: A325237 A358071 A065799 * A123098 A351716 A136699

Adjacent sequences: A162579 A162580 A162581 * A162583 A162584 A162585

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2009

Status

approved