OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..201
FORMULA
E.g.f. A(x) satisfies: A'(x) = A(A(x) - 1)^3. - Paul D. Hanna, Aug 26 2024
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 24*x^3/3! + 339*x^4/4! + 7101*x^5/5! + 200961*x^6/6! + 7256277*x^7/7! + 321662502*x^8/8! + ...
where A(x) = 1 + Series_Reversion( Integral 1/A(x)^3 dx ).
RELATED SERIES.
Integral 1/A(x)^3 dx = x - 3*x^2/2! + 3*x^3/3! - 24*x^4/4! - 261*x^5/5! - 6543*x^6/6! - 202671*x^7/7! - 7911351*x^8/8! + ...
where Integral 1/A(x)^3 dx = Series_Reversion(A(x) - 1).
A(A(x) - 1) = 1 + x + 6*x^2/2! + 75*x^3/3! + 1479*x^4/4! + 40617*x^5/5! + 1447785*x^6/6! + 64027656*x^7/7! + 3404869020*x^8/8! + ...
A(A(x) - 1)^3 = 1 + 3*x + 24*x^2/2! + 339*x^3/3! + 7101*x^4/4! + ...
where A(A(x) - 1)^3 = d/dx A(x).
PROG
(PARI) {a(n) = my(A=1+x+x*O(x^n)); for(i=0, n, A = 1 + serreverse(intformal(1/A^3))); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 07 2008
STATUS
approved