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Search: id:A162585
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| A162585 |
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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. |
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1
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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).
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EXAMPLE
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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 +...
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PROGRAM
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(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)}
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CROSSREFS
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Cf. A000108, A000984, A006519, A000123.
Sequence in context: A091004 A005559 A001471 this_sequence A000159 A090612 A051744
Adjacent sequences: A162582 A162583 A162584 this_sequence A162586 A162587 A162588
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2009
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