A162585 G.f.: A(x) = exp( Sum_{n>=1} C(2n,n)*A006519(n) * x^n/n ), where A006519(n) = highest power of 2 dividing n.

1, 2, 8, 20, 114, 288, 1156, 3256, 23464, 59716, 243212, 699216, 3659988, 10265800, 42353168, 128163440, 1127515970, 2858004752, 11768578868, 34294832344, 180335471424, 513911386232, 2137413847256, 6572758142016, 41948816796852

Offset

0,2

Comments

Compare g.f. to the g.f. of the Catalan numbers: exp( Sum_{n>=1} C(2n,n)*x^n/n ), where C(2n,n) form the central binomial coefficients (A000984).

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 + 146*x^4 + 282*x^5 + 826*x^6 + ...
log(A(x)) = 2*x + 12*x^2/2 + 20*x^3/3 + 280*x^4/4 + 252*x^5/5 + 1848*x^6/6 + ... + C(2n,n)*A006519(n)*x^n/n + ...

Mathematica

nmax=50; CoefficientList[Series[Exp[Sum[2^(IntegerExponent[k, 2])*Binomial[2*k, k]*q^k/k, {k, nmax+3}]], {q, 0, nmax}], q]  (* G. C. Greubel, Jul 04 2018 *)

Prog

(PARI) {a(n)=local(L=sum(m=1, n, 2^valuation(m, 2)*binomial(2*m, m)*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

Crossrefs

Cf. A000108, A000123, A000984, A006519.

Sequence in context: A091004 A005559 A001471 * A000159 A358681 A090612

Adjacent sequences: A162582 A162583 A162584 * A162586 A162587 A162588

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2009

Status

approved