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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
1, 1, 4, 29, 312, 4528, 83736, 1899663, 51453040, 1630256006, 59469464760, 2465840319140, 114998710427424, 5979178955915340, 343988093896335456, 21756022936437138621, 1504147473897522799968, 113112315128397169399144, 9211153567415833154691864, 809061792101088872463677754 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..100

EXAMPLE

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

PROG

(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)}

CROSSREFS

Cf. A194956, A195195, A195196.

Sequence in context: A030019 A303928 A201627 * A215955 A295237 A028853

Adjacent sequences:  A195191 A195192 A195193 * A195195 A195196 A195197

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 11 2011

STATUS

approved

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Last modified May 26 01:32 EDT 2022. Contains 354073 sequences. (Running on oeis4.)