OFFSET
0,3
FORMULA
E.g.f.: A(x)=1/Q(0); Q(k)=1-x/((3*k+1)-(x^2)*(3*k+1)/((x^2)+3*(3*k+2)*(k+1)/Q(k+1)))) ; (continued fraction). - Sergei N. Gladkovskii, Nov 26 2011
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 31*x^4/4! + 170*x^5/5! +...
where
A(x) = 1/(1 - x - x^3/3! + x^4/4! + x^6/6! - x^7/7! - x^9/9! + x^10/10! +...).
PROG
(PARI) {a(n)=n!*polcoeff(1/(exp(-x+x*O(x^n)) - sum(m=0, n\3, (-x)^(3*m+2)/(3*m+2)! )), n)}
(PARI) {a(n)=n!*polcoeff(1/(sum(m=0, n\3+1, (-x)^(3*m)/(3*m)! + (-x)^(3*m+1)/(3*m+1)! +x^2*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 09 2011
STATUS
approved