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Search: id:A158053
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| A158053 |
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G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x*A(x))^n * x^n/n ). |
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1
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| 1, 1, 3, 9, 37, 183, 1175, 10405, 132911, 2533697, 70988149, 2886198771, 168860266189, 14046492509383, 1668792185650203, 280222608364043833, 66930106539423614233, 22572046654805538142763
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Compare to: M(x) = exp( Sum_{n>=1} (1 + x*M(x))^n * x^n/n ) where M(x) is the g.f. of the Motzkin numbers (A001006).
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 37*x^4 + 183*x^5 + 1175*x^6 +...
log(A(x)) = x + 5*x^2/2 + 19*x^3/3 + 105*x^4/4 + 671*x^5/5 + 5525*x^6/6 +...
log(A(x)) = (1+2x*A(x))*x + (1+4x*A(x))^2*x^2/2 + (1+8x*A(x))^3*x^3/3 +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (1+2^m*x*A)^m*x^m/m+x*O(x^n)))); polcoeff(A, n)}
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CROSSREFS
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Cf. A156214.
Sequence in context: A006229 A008986 A105215 this_sequence A009179 A030819 A030904
Adjacent sequences: A158050 A158051 A158052 this_sequence A158054 A158055 A158056
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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), Mar 11 2009
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