A196022 E.g.f. satisfies: A(x) = Sum_{n>=0} 1/n! * Sum_{k=0..n} C(n,k)*(1 + x/2*A(x)^(n-k))^(n-k) * (-1 + x/2*A(x)^k)^k.

1, 1, 3, 22, 269, 4676, 106027, 2966909, 98814921, 3818572219, 167999566061, 8292669672343, 453958089569833, 27300462412168531, 1789601591598075179, 127031469572649790786, 9709396866317453042033, 795229841271312470470904, 69499103185446754949076817

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4676*x^5/5! +...
where e.g.f. A = A(x) satisfies:
A(x) = 1 + ((1+x/2*A) + (-1+x/2*A)) +
1/2!*((1+x/2*A^2)^2 + 2*(1+x/2*A)*(-1+x/2*A) + (-1+x/2*A^2)^2) +
1/3!*((1+x/2*A^3)^3 + 3*(1+x/2*A^2)^2*(-1+x/2*A) + 3*(1+x/2*A)*(-1+x/2*A^2)^2 + (-1+x/2*A^3)^3) +
1/4!*((1+x/2*A^4)^4 + 4*(1+x/2*A^3)^3*(-1+x/2*A) + 6*(1+x/2*A^2)^2*(-1+x/2*A^2)^2 + 4*(1+x/2*A)*(-1+x/2*A^3)^3 + (-1+x/2*A^4)^4) +
1/5!*((1+x/2*A^5)^5 + 5*(1+x/2*A^4)^4*(-1+x/2*A) + 10*(1+x/2*A^3)^3*(-1+x/2*A^2)^2 + 10*(1+x/2*A^2)^2*(-1+x/2*A^3)^3 + 5*(1+x/2*A)*(-1+x/2*A^4)^4 + (-1+x/2*A^5)^5) +...

Prog

(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, 1/m!*sum(k=0, m, binomial(m, k)*(1+X/2*A^(m-k))^(m-k)*(-1+X/2*A^k)^k))); n!*polcoeff(A, n)}

Crossrefs

Sequence in context: A195512 A052892 A155806 * A319147 A074706 A293989

Adjacent sequences: A196019 A196020 A196021 * A196023 A196024 A196025

Keyword

nonn

Author

Paul D. Hanna, Sep 26 2011

Status

approved