A196497 G.f. satisfies: A( x*A(-x)/A(x) ) = 1 + x.

1, 1, 2, 6, 30, 170, 1242, 9534, 86118, 797778, 8327410, 88438966, 1032534190, 12233231738, 156832510922, 2038914853870, 28368720701302, 400233587440290, 5994141844357346, 91033137985948774, 1458360235236325182, 23691777860254217802, 403933868741833240506

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

G.f. satisfies: A(x) = 1 + x*A(A(x) - 1)/A(1 - A(x)).

Example

 G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 30*x^4 + 170*x^5 + 1242*x^6 +...
Related expansions.
x*A(-x)/A(x) = x - 2*x^2 + 2*x^3 - 10*x^4 + 18*x^5 - 290*x^6 + 594*x^7 +...
A(A(x)-1) = 1 + x + 4*x^2 + 20*x^3 + 128*x^4 + 928*x^5 + 7636*x^6 +...
A(1-A(x)) = 1 - x - 4*x^3 - 4*x^4 - 112*x^5 - 288*x^6 - 6436*x^7 +...

Prog

 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+serreverse(x*subst(A, x, -x)/(A+x*O(x^n)))); polcoeff(A, n)}

Crossrefs

Sequence in context: A057221 A180892 A366266 * A127115 A290354 A293906

Adjacent sequences: A196494 A196495 A196496 * A196498 A196499 A196500

Keyword

nonn

Author

Paul D. Hanna, Oct 04 2011

Status

approved