A212527 G.f. satisfies: A(x) = 1 + x*A(x)^2 / (A(I*x) * A(-I*x)).

1, 1, 2, 8, 26, 56, 194, 832, 2866, 7904, 30690, 137000, 497706, 1491512, 6041602, 27557184, 102985186, 321675648, 1333006018, 6160815624, 23426000186, 75016874488, 315357132994, 1470462300160, 5656904907026, 18419315779552, 78201118018466, 366962271138472

Offset: 0

Author

Paul D. Hanna, Jun 13 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 26*x^4 + 56*x^5 + 194*x^6 + 832*x^7 +...
Related expansions begin:
A(x)^2 = 1 + 2*x + 5*x^2 + 20*x^3 + 72*x^4 + 196*x^5 + 668*x^6 + 2692*x^7 +...
A(I*x)*A(-I*x) = 1 - 3*x^2 + 40*x^4 - 316*x^6 + 4624*x^8 - 50676*x^10 + 811192*x^12 -+...
		

Crossrefs

Cf. A143339, A216681, A216712, A216713.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+x*A^2/(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),", "))