A196711 G.f.: A(x) = INV(x-x^2 - x^2*INV(x-2*x^2 - x^2*INV(x-4*x^2 - x^2*INV(x-8*x^2 - x^2*INV(x-16*x^2 - ...))))), where INV(F(x)) = series reversion of F(x).

1, 1, 3, 12, 59, 341, 2274, 17380, 152492, 1546370, 18253752, 251911212, 4077747676, 77875414462, 1766771227627, 47719589665506, 1529956518699126, 58172058892474403, 2633354766431360249, 142248925696032886182, 9135446223074433352932, 695222497681195469397031

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Example

 G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 59*x^5 + 341*x^6 + 2274*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 + 54*x^4 + 392*x^5 + 3358*x^6 + 33768*x^7 +...
B(x) = Series_Reversion(x-2*x^2 - x^2*C(x)), where
C(x) = x + 4*x^2 + 33*x^3 + 348*x^4 + 4244*x^5 + 58364*x^6 + 911064*x^7 +...
C(x) = Series_Reversion(x-4*x^2 - x^2*D(x)), where
D(x) = x + 8*x^2 + 129*x^3 + 2616*x^4 + 59972*x^5 + 1497592*x^6 +...
D(x) = Series_Reversion(x-8*x^2 - x^2*E(x)), where
E(x) = x + 16*x^2 + 513*x^3 + 20592*x^4 + 928004*x^5 + 45007856*x^6 +...
E(x) = Series_Reversion(x-16*x^2 - x^2*F(x)), where
F(x) = x + 32*x^2 + 2049*x^3 + 164064*x^4 + 14722052*x^5 + 1417021408*x^6 +...

Prog

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

Crossrefs

Cf. A196710.

Sequence in context: A064856 A080337 A196710 * A304788 A101054 A122752

Adjacent sequences: A196708 A196709 A196710 * A196712 A196713 A196714

Keyword

nonn

Author

Paul D. Hanna, Oct 05 2011

Status

approved