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 A195194 G.f.: A(x) = INV(x - x*INV(x - 2*x*INV(x - 3*x*INV(x - 4*x*INV(x - ...))))), where INV(F(x)) = series reversion of F(x). 4

%I

%S 1,1,4,29,312,4528,83736,1899663,51453040,1630256006,59469464760,

%T 2465840319140,114998710427424,5979178955915340,343988093896335456,

%U 21756022936437138621,1504147473897522799968,113112315128397169399144,9211153567415833154691864,809061792101088872463677754

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

%H Paul D. Hanna, <a href="/A195194/b195194.txt">Table of n, a(n) for n = 1..100</a>

%e G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 312*x^4 + 4528*x^5 + 83736*x^6 +...

%e where A(x) results from nested inversions of shifted series:

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

%e B(x) = x + 2*x^2 + 14*x^3 + 160*x^4 + 2498*x^5 + 49344*x^6 +...;

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

%e C(x) = x + 3*x^2 + 30*x^3 + 471*x^4 + 9762*x^5 + 248346*x^6 +...;

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

%e D(x) = x + 4*x^2 + 52*x^3 + 1040*x^4 + 26964*x^5 + 843808*x^6 +...;

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

%e E(x) = x + 5*x^2 + 80*x^3 + 1945*x^4 + 60620*x^5 + 2256660*x^6 +...;

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

%e F(x) = x + 6*x^2 + 114*x^3 + 3264*x^4 + 118902*x^5 + 5136768*x^6 +...;

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

%e G(x) = x + 7*x^2 + 154*x^3 + 5075*x^4 + 211638*x^5 + 10413214*x^6 +...;

%e G(x) = Series_Reversion(x - 7*x*H(x)), where

%e H(x) = x + 8*x^2 + 200*x^3 + 7456*x^4 + 350312*x^5 + 19344576*x^6 +...; ...

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

%Y Cf. A194956, A195195, A195196.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Sep 11 2011

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Last modified July 2 10:07 EDT 2022. Contains 355004 sequences. (Running on oeis4.)