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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 06 2009
STATUS
approved