OFFSET
0,3
FORMULA
G.f.: 1 + Series_Reversion(x - 6*x^2 - 15*x^3 - 14*x^4 - 6*x^5 - x^6).
EXAMPLE
G.f.: A(x) = 1 + x + 6*x^2 + 87*x^3 + 1544*x^4 + 30669*x^5 +...
Related expansions.
A(x)^3 = 1 + 3*x + 21*x^2 + 298*x^3 + 5280*x^4 + 104772*x^5 +...
A(x)^4 = 1 + 4*x + 30*x^2 + 424*x^3 + 7509*x^4 + 148968*x^5 +...
A(x)^6 = 1 + 6*x + 51*x^2 + 722*x^3 + 12789*x^4 + 253740*x^5 +...
where 1+x = A(x)^3 + A(x)^4 - A(x)^6.
PROG
(PARI) /* From 1+x = A(x)^3 + A(x)^4 - A(x)^6: */
{a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^3+Ser(A)^4-Ser(A)^6)[#A]); A[n+1]}
for(n=0, 25, print1(a(n) , ", "))
(PARI) /* From Series Reversion: */
{a(n)=local(A=1+serreverse(x - 6*x^2 - 15*x^3 - 14*x^4 - 6*x^5 - x^6 + x^2*O(x^n))); polcoeff(A, n)}
for(n=0, 25, print1(a(n) , ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 27 2014
STATUS
approved