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A240998
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G.f. satisfies: A(x)^2 = x + A(x + 2*x^2).
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1
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1, 1, 1, 2, 11, 86, 942, 12996, 217179, 4258118, 95807186, 2432620268, 68794640758, 2144208839932, 73022589819004, 2697651739347912, 107445653707814259, 4589616491007605958, 209295193019035187754, 10148293234344417217692, 521357263631063209544130
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OFFSET
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0,4
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COMMENTS
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For n>0, a(n) == 1 (mod 2) iff n=2^k for k>=0 (conjecture).
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LINKS
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FORMULA
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a(n) ~ c * 2^n * n^(n - 1 - log(2)) / (exp(n) * (log(2))^n), where c = 0.223600492535213287429897519... . - Vaclav Kotesovec, Aug 08 2014
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EXAMPLE
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G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 11*x^4 + 86*x^5 + 942*x^6 + 12996*x^7 +...
Compare the related series:
A(x)^2 = 1 + 2*x + 3*x^2 + 6*x^3 + 27*x^4 + 198*x^5 + 2082*x^6 + 28092*x^7 +...
A(x+2*x^2) = 1 + x + 3*x^2 + 6*x^3 + 27*x^4 + 198*x^5 + 2082*x^6 + 28092*x^7 +...
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PROG
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(PARI) {a(n)=local(A=[1, 1], Ax=Ser(A)); for(i=1, n, A=concat(A, 0);
A[#A]=Vec(1+subst(Ser(A), x, x+2*x^2) - Ser(A)^2)[#A]); A[n+1]}
for(n=0, 25, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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