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A156214
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G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*(x*A(x))^n/n ), a power series in x with integer coefficients.
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2
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1, 2, 14, 256, 18734, 6932928, 11550075900, 80606017093632, 2307293302418365718, 268696321569450570148864, 126770971088210751226430473604, 241680859880056839468193961216049152
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OFFSET
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0,2
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COMMENTS
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Compare to g.f. for Catalan sequence: C(x) = exp( Sum_{n>=1} (x*C(x))^n/n ).
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LINKS
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Table of n, a(n) for n=0..11.
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FORMULA
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G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where A(x*G(x)) = G(x) is the g.f. of A155200. [From Paul D. Hanna, Jun 30 2009]
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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 14*x^2 + 256*x^3 + 18734*x^4 + 6932928*x^5 +...
log(A(x)) = 2*x + 24*x^2/2 + 692*x^3/3 + 72704*x^4/4 + 34465932*x^5/5 +...
log(A(x)) = 2*xA(x) + 2^4*(xA(x))^2/2 + 2^9*(xA(x))^3/3 + 2^16*(xA(x))^4/4 + ...
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(sum(k=1, n, (2^k*x*A)^k/k))); polcoeff(A, n)}
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CROSSREFS
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Cf. A000108, A156213.
Sequence in context: A219344 A152476 A070813 * A187654 A015197 A156910
Adjacent sequences: A156211 A156212 A156213 * A156215 A156216 A156217
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Feb 06 2009
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STATUS
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approved
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