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A196710 G.f.: A(x) = INV(x-x^2 - x^2*INV(x-2*x^2 - x^2*INV(x-3*x^2 - x^2*INV(x-4*x^2 - x^2*INV(x-5*x^2 - ...))))), where INV(F(x)) = series reversion of F(x). 2
1, 1, 3, 12, 59, 340, 2240, 16583, 136185, 1229220, 12119025, 129957670, 1510458859, 18958901987, 255980593558, 3703327622812, 57208927916093, 941005426734340, 16442518936115083, 304566619900207724, 5967901050385272977, 123436972340208737237, 2689201938559338920299 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 59*x^5 + 340*x^6 + 2240*x^7 +...

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

A(x) = Series_Reversion(x-x^2 - x^2*B(x)), where

B(x) = x + 2*x^2 + 9*x^3 + 53*x^4 + 366*x^5 + 2849*x^6 + 24591*x^7 +...

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

C(x) = x + 3*x^2 + 19*x^3 + 154*x^4 + 1431*x^5 + 14632*x^6 + 161808*x^7 +...

C(x) = Series_Reversion(x-3*x^2 - x^2*D(x)), where

D(x) = x + 4*x^2 + 33*x^3 + 345*x^4 + 4094*x^5 + 52855*x^6 + 728291*x^7 +...

D(x) = Series_Reversion(x-4*x^2 - x^2*E(x)), where

E(x) = x + 5*x^2 + 51*x^3 + 656*x^4 + 9531*x^5 + 149804*x^6 + 2495784*x^7 +...

E(x) = Series_Reversion(x-5*x^2 - x^2*F(x)), where

F(x) = x + 6*x^2 + 73*x^3 + 1117*x^4 + 19254*x^5 + 357925*x^6 + 7026015*x^7 +...

F(x) = Series_Reversion(x-6*x^2 - x^2*G(x)), where

G(x) = x + 7*x^2 + 99*x^3 + 1758*x^4 + 35111*x^5 + 754864*x^6 + 17098376*x^7 +...

PROG

(PARI) {a(n)=local(G=x+x^2); for(k=0, n, G=serreverse(x-(n-k+1)*x^2 - x^2*G+x^3*O(x^n))); polcoeff(G, n)}

CROSSREFS

Cf. A196711.

Sequence in context: A179325 A064856 A080337 * A196711 A304788 A101054

Adjacent sequences:  A196707 A196708 A196709 * A196711 A196712 A196713

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 05 2011

STATUS

approved

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Last modified May 14 04:22 EDT 2021. Contains 343872 sequences. (Running on oeis4.)