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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
1, 1, 2, 6, 20, 73, 281, 1125, 4636, 19540, 83848, 365107, 1609285, 7166523, 32195965, 145746024, 664165843, 3044370240, 14027289780, 64932957320, 301833739881, 1408338395737, 6593747768053, 30967985680291, 145859467298446, 688805924907628, 3260700755258527 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..500 (terms 1..210 from Paul D. Hanna)

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 5.023750195318838381709... and c = 0.049554511600191... - Vaclav Kotesovec, Sep 02 2017

EXAMPLE

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

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

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

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

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

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

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

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

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

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

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

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

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

PROG

(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)}

CROSSREFS

Sequence in context: A230823 A192497 A104632 * A150141 A150142 A150143

Adjacent sequences:  A194953 A194954 A194955 * A194957 A194958 A194959

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 07 2011

STATUS

approved

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Last modified January 23 13:57 EST 2022. Contains 350511 sequences. (Running on oeis4.)