OFFSET
1,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..100
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 312*x^4 + 4528*x^5 + 83736*x^6 +...
where A(x) results from nested inversions of shifted series:
A(x) = Series_Reversion(x - x*B(x)), where
B(x) = x + 2*x^2 + 14*x^3 + 160*x^4 + 2498*x^5 + 49344*x^6 +...;
B(x) = Series_Reversion(x - 2*x*C(x)), where
C(x) = x + 3*x^2 + 30*x^3 + 471*x^4 + 9762*x^5 + 248346*x^6 +...;
C(x) = Series_Reversion(x - 3*x*D(x)), where
D(x) = x + 4*x^2 + 52*x^3 + 1040*x^4 + 26964*x^5 + 843808*x^6 +...;
D(x) = Series_Reversion(x - 4*x*E(x)), where
E(x) = x + 5*x^2 + 80*x^3 + 1945*x^4 + 60620*x^5 + 2256660*x^6 +...;
E(x) = Series_Reversion(x - 5*x*F(x)), where
F(x) = x + 6*x^2 + 114*x^3 + 3264*x^4 + 118902*x^5 + 5136768*x^6 +...;
F(x) = Series_Reversion(x - 6*x*G(x)), where
G(x) = x + 7*x^2 + 154*x^3 + 5075*x^4 + 211638*x^5 + 10413214*x^6 +...;
G(x) = Series_Reversion(x - 7*x*H(x)), where
H(x) = x + 8*x^2 + 200*x^3 + 7456*x^4 + 350312*x^5 + 19344576*x^6 +...; ...
PROG
(PARI) {a(n)=local(G=x+x^2); for(k=0, n, G=serreverse(x-(n-k+1)*x*G+x*O(x^n))); polcoeff(G, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 11 2011
STATUS
approved