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