A196708 G.f.: A(x) = INV(x*(1-x) - x^2*INV(x*(1-x)^2 - x^2*INV(x*(1-x)^3 - x^2*INV(x*(1-x)^4 - x^2*INV(x*(1-x)^5 - ...))))), where INV(F(x)) = series reversion of F(x).

1, 1, 3, 12, 58, 323, 2026, 14125, 108472, 911203, 8326290, 82382317, 879231033, 10088749986, 124101412790, 1632187723201, 22895274500999, 341738132438907, 5415659970194984, 90928786402251744, 1614244644876588572, 30243386104969900766, 596915061724923842269

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 + 58*x^5 + 323*x^6 + 2026*x^7 +...
where A(x) results from nested inversions of shifted series:
A(x) = Series_Reversion(x*(1-x) - x^2*B(x)), where
B(x) = x + 2*x^2 + 8*x^3 + 43*x^4 + 276*x^5 + 2014*x^6 + 16313*x^7 +...
B(x) = Series_Reversion(x*(1-x)^2 - x^2*C(x)), where
C(x) = x + 3*x^2 + 16*x^3 + 110*x^4 + 885*x^5 + 7992*x^6 + 79339*x^7 +...
C(x) = Series_Reversion(x*(1-x)^3 - x^2*D(x)), where
D(x) = x + 4*x^2 + 27*x^3 + 229*x^4 + 2235*x^5 + 24181*x^6 + 284809*x^7 +...
D(x) = Series_Reversion(x*(1-x)^4 - x^2*E(x)), where
E(x) = x + 5*x^2 + 41*x^3 + 416*x^4 + 4801*x^5 + 60825*x^6 + 831773*x^7 +...
E(x) = Series_Reversion(x*(1-x)^5 - x^2*F(x)), where
F(x) = x + 6*x^2 + 58*x^3 + 687*x^4 + 9183*x^5 + 133784*x^6 + 2089453*x^7 +...
F(x) = Series_Reversion(x*(1-x)^6 - x^2*G(x)), where
G(x) = x + 7*x^2 + 78*x^3 + 1058*x^4 + 16106*x^5 + 265830*x^6 + 4678877*x^7 +...

Prog

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

Crossrefs

Cf. A194956, A196709.

Sequence in context: A090363 A115086 A258173 * A184511 A125276 A001426

Adjacent sequences: A196705 A196706 A196707 * A196709 A196710 A196711

Keyword

nonn

Author

Paul D. Hanna, Oct 05 2011

Status

approved