A196734 E.g.f. satisfies: A(x) = exp(x*A(2*x)^(1/2)).

1, 1, 3, 22, 377, 15236, 1458577, 326046946, 166826961233, 192154584592072, 491898410990385281, 2770349200953966300494, 34041983929934523771795481, 906333341309409985333411618492, 51972772881917637838407651811301201, 6386414140694907598544170345261596881026

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f.: A(x) = G(x/2)^2 where G(x) = e.g.f. of A096538.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 377*x^4/4! + 15236*x^5/5! +...
where
A(2*x)^(1/2) = 1 + x + 5*x^2/2! + 73*x^3/3! + 2649*x^4/4! + 226881*x^5/5! + 45061213*x^6/6! +...+ A096538(n)*x^n/n! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, 21, A=exp(x*subst(A, x, 2*x+x*O(x^n))^(1/2))); n!*polcoeff(A, n)}

Crossrefs

Cf. A096538, A196735.

Sequence in context: A219268 A259919 A275366 * A271849 A271850 A364844

Adjacent sequences: A196731 A196732 A196733 * A196735 A196736 A196737

Keyword

nonn

Author

Paul D. Hanna, Oct 05 2011

Status

approved