A196709 G.f.: A(x) = INV(x - x*INV(x - 2*x^2*INV(x - 3*x^3*INV(x - 4*x^4*INV(x - ...))))), where INV(F(x)) = series reversion of F(x).

1, 1, 2, 7, 26, 110, 490, 2289, 11032, 54566, 275290, 1411846, 7339180, 38588752, 204877804, 1096919969, 5916055860, 32113211082, 175311638256, 961935749512, 5302286426878, 29347327341840, 163040493728376, 908865025329612, 5082227505135978, 28500261134798892

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 26*x^5 + 110*x^6 + 490*x^7 +...
where A(x) results from nested inversions of shifted series:
A(x) = Series_Reversion(x - x*B(x)), where
B(x) = x + 2*x^3 + 12*x^5 + 6*x^6 + 96*x^7 + 108*x^8 + 952*x^9 +...
B(x) = Series_Reversion(x - 2*x^2*C(x)), where
C(x) = x + 3*x^4 + 36*x^7 + 12*x^8 + 594*x^10 + 432*x^11 + 240*x^12 +...
C(x) = Series_Reversion(x - 3*x^3*D(x)), where
D(x) = x + 4*x^5 + 80*x^9 + 20*x^10 + 2240*x^13 + 1200*x^14 + 600*x^15 +...
D(x) = Series_Reversion(x - 4*x^4*E(x)), where
E(x) = x + 5*x^6 + 150*x^11 + 30*x^12 + 6375*x^16 + 2700*x^17 + 1260*x^18 +...
E(x) = Series_Reversion(x - 5*x^5*F(x)), where
F(x) = x + 6*x^7 + 252*x^13 + 42*x^14 + 15120*x^19 + 5292*x^20 + 2352*x^21 +...
F(x) = Series_Reversion(x - 6*x^6*G(x)), where
G(x) = x + 7*x^8 + 392*x^15 + 56*x^16 + 31556*x^22 + 9408*x^23 + 4032*x^24 +...

Prog

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

Crossrefs

Cf. A194956, A196710, A196708.

Sequence in context: A150584 A150585 A150586 * A150587 A001862 A150588

Adjacent sequences: A196706 A196707 A196708 * A196710 A196711 A196712

Keyword

nonn

Author

Paul D. Hanna, Oct 05 2011

Status

approved