A216681 G.f.: A(x) = 1 + x*A(x)^3 / ( A(I*x)*A(-I*x) ), where I^2 = -1.

1, 1, 3, 17, 85, 333, 1883, 13153, 76329, 363033, 2304867, 17067553, 104686957, 534812789, 3558451915, 27086552833, 170930393745, 906063493617, 6183676880195, 47831931663921, 307091159448965, 1664876216837789, 11545009017568635, 90248125157828449

Offset: 0

Author

Paul D. Hanna, Sep 14 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 85*x^4 + 333*x^5 + 1883*x^6 +...
Related expansions:
A(x)^2 = 1 + 2*x + 7*x^2 + 40*x^3 + 213*x^4 + 938*x^5 + 5231*x^6 +...
A(x)^3 = 1 + 3*x + 12*x^2 + 70*x^3 + 393*x^4 + 1893*x^5 + 10632*x^6 +...
A(x)*A(-x) = 1 + 5*x^2 + 145*x^4 + 3321*x^6 + 133553*x^8 + 4103661*x^10 +...
A(I*x)*A(-I*x) = 1 - 5*x^2 + 145*x^4 - 3321*x^6 + 133553*x^8 - 4103661*x^10 + 184486609*x^12 - 6359604209*x^14 + 302240850145*x^16 - 11073953305621*x^18 +...
Note that a bisection of 1/A(x)^2 equals a bisection of 1/A(x)^3:
1/A(x)^2 = 1 - 2*x - 3*x^2 - 20*x^3 - 72*x^4 - 108*x^5 - 1196*x^6 +...
1/A(x)^3 = 1 - 3*x - 3*x^2 - 25*x^3 - 72*x^4 + 12*x^5 - 1196*x^6 +...
		

Crossrefs

Cf. A212527, A216712, A216713.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=1+x*A^3/(subst(A, x, I*x+x*O(x^n))*subst(A, x, -I*x+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))