OFFSET
1,3
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 05 2011
STATUS
approved