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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
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 (list; graph; refs; listen; history; text; internal format)
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 = 150; a[n_]:= SeriesCoefficient[Series[Exp[Sum[2^(IntegerExponent[k, 2])*Binomial[2*k, k]*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^valuation(m, 2)*binomial(2*m, m)*x^m/m)+x*O(x^n)); polcoeff(exp(L), n)}

CROSSREFS

Cf. A000108, A000984, A006519, A000123.

Sequence in context: A091004 A005559 A001471 * A000159 A090612 A212981

Adjacent sequences:  A162582 A162583 A162584 * A162586 A162587 A162588

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 06 2009

STATUS

approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)