OFFSET
0,3
COMMENTS
Compare to e.g.f. F(x) of A183611, which satisfies F'(x) = F(x)^2 + x*F(x)^3, where F(x) = d/dx Series_Reversion( Sum_{n>=1} x^(3*n-2)/(3*n-2)! - x^(3*n-1)/(3*n-1)! ).
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 119*x^4/4! + 1134*x^5/5! +...
E.g.f.: A(x) = d/dx Series_Reversion(G(x)) where G(x) begins:
G(x) = x - x^2/2! - x^4/4! + x^5/5! + x^7/7! - x^8/8! - x^10/10! + x^11/11! +...
The series reversion of G(x) begins:
x + x^2/2! + 3*x^3/3! + 16*x^4/4! + 119*x^5/5! + 1134*x^6/6! +...
PROG
(PARI) {a(n)=n!*polcoeff(deriv(serreverse(sum(m=0, n\3+1, (-x)^(3*m)/(3*m)!)-exp(-x+x^2*O(x^n)))), n)}
(PARI) {a(n)=n!*polcoeff(deriv(serreverse(sum(m=1, n\3+1, -(-x)^(3*m-2)/(3*m-2)!-(-x)^(3*m-1)/(3*m-1)!+x^2*O(x^n)))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 08 2011
STATUS
approved