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 A194956 G.f.: A(x) = INV(x - x*INV(x - x^2*INV(x - x^3*INV(x - x^4*INV(x - ...))))), where INV(F(x)) = series reversion of F(x). 6

%I

%S 1,1,2,6,20,73,281,1125,4636,19540,83848,365107,1609285,7166523,

%T 32195965,145746024,664165843,3044370240,14027289780,64932957320,

%U 301833739881,1408338395737,6593747768053,30967985680291,145859467298446,688805924907628,3260700755258527

%N G.f.: A(x) = INV(x - x*INV(x - x^2*INV(x - x^3*INV(x - x^4*INV(x - ...))))), where INV(F(x)) = series reversion of F(x).

%H Vaclav Kotesovec, <a href="/A194956/b194956.txt">Table of n, a(n) for n = 1..500</a> (terms 1..210 from Paul D. Hanna)

%F a(n) ~ c * d^n / n^(3/2), where d = 5.023750195318838381709... and c = 0.049554511600191... - _Vaclav Kotesovec_, Sep 02 2017

%e G.f.: A(x) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 73*x^6 + 281*x^7 +...

%e Series_Reversion(A(x)) = x - x*B(x) where

%e B(x) = x + x^3 + 3*x^5 + x^6 + 12*x^7 + 9*x^8 + 59*x^9 + 67*x^10 +...

%e Series_Reversion(B(x)) = x - x^2*C(x) where

%e C(x) = x + x^4 + 4*x^7 + x^8 + 22*x^10 + 12*x^11 + 5*x^12 + 141*x^13 +...

%e Series_Reversion(C(x)) = x - x^3*D(x) where

%e D(x) = x + x^5 + 5*x^9 + x^10 + 35*x^13 + 15*x^14 + 6*x^15 + x^16 +...

%e Series_Reversion(D(x)) = x - x^4*E(x) where

%e E(x) = x + x^6 + 6*x^11 + x^12 + 51*x^16 + 18*x^17 + 7*x^18 + x^19 +...

%e Series_Reversion(E(x)) = x - x^5*F(x) where

%e F(x) = x + x^7 + 7*x^13 + x^14 + 70*x^19 + 21*x^20 + 8*x^21 + x^22 +...

%e Series_Reversion(F(x)) = x - x^6*G(x) where

%e G(x) = x + x^8 + 8*x^15 + x^16 + 92*x^22 + 24*x^23 + 9*x^24 + x^25 +...

%o (PARI) {a(n)=local(G=x); m=sqrtint(2*n+1);for(k=0,m, G=serreverse(x-x^(m-k+1)*G+x*O(x^n))); polcoeff(G, n)}

%K nonn

%O 1,3

%A _Paul D. Hanna_, Sep 07 2011

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Last modified May 24 11:04 EDT 2022. Contains 354033 sequences. (Running on oeis4.)