A196659 G.f.: A(x) = INV(x - x*INV(x - 3*x*INV(x - 5*x*INV(x - 7*x*INV(x - ...))))), where INV(F(x)) = series reversion of F(x).

1, 1, 5, 53, 917, 22617, 735033, 29953065, 1479692909, 86472860573, 5868283305245, 455754185294737, 40032598733260945, 3938398783862213521, 430402127790139060725, 51882414924375353368677, 6856582955062676722110885, 988136808489380086666701225

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Example

G.f.: A(x) = x + x^2 + 5*x^3 + 53*x^4 + 917*x^5 + 22617*x^6 +...
where A(x) results from nested inversions of shifted series:
A(x) = Series_Reversion(x - x*B(x)), where
B(x) = x + 3*x^2 + 33*x^3 + 615*x^4 + 16149*x^5 + 550431*x^6 +...;
B(x) = Series_Reversion(x - 3*x*C(x)), where
C(x) = x + 5*x^2 + 85*x^3 + 2305*x^4 + 83685*x^5 + 3776885*x^6 +...;
C(x) = Series_Reversion(x - 5*x*D(x)), where
D(x) = x + 7*x^2 + 161*x^3 + 5747*x^4 + 268037*x^5 + 15199611*x^6 +...;
D(x) = Series_Reversion(x - 7*x*E(x)), where
E(x) = x + 9*x^2 + 261*x^3 + 11565*x^4 + 660213*x^5 + 45228753*x^6 +...;
E(x) = Series_Reversion(x - 9*x*F(x)), where
F(x) = x + 11*x^2 + 385*x^3 + 20383*x^4 + 1377717*x^5 + 110795927*x^6 +...;
F(x) = Series_Reversion(x - 11*x*G(x)), where
G(x) = x + 13*x^2 + 533*x^3 + 32825*x^4 + 2564549*x^5 + 236963181*x^6 +...;
G(x) = Series_Reversion(x - 13*x*H(x)), where
H(x) = x + 15*x^2 + 705*x^3 + 49515*x^4 + 4391205*x^5 + 458531955*x^6 +...; ...

Prog

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

Crossrefs

Cf. A195194.

Sequence in context: A357343 A377323 A231866 * A128943 A180351 A337151

Adjacent sequences: A196656 A196657 A196658 * A196660 A196661 A196662

Keyword

nonn

Author

Paul D. Hanna, Oct 05 2011

Status

approved