A208889 G.f. satisfies: A(x) = 1 + x*A(x)/A(-x) + x^2*A(x)*A(-x).

1, 1, 3, 2, 5, -2, 3, -20, -2, -38, 75, 84, 612, 596, 2293, 534, 4722, -6354, 6716, -27696, 44962, -8232, 391279, 310072, 1975046, 906028, 6363470, -2135522, 15639296, -21729494, 57269753, -46268934, 370270484, 130699742, 2081100420, 915348168, 8523787094

Offset: 0

Author

Paul D. Hanna, Mar 09 2012

Keywords

• sign

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 2*x^3 + 5*x^4 - 2*x^5 + 3*x^6 - 20*x^7 +...
Related series:
A(x)/A(-x) = 1 + 2*x + 2*x^2 - 2*x^4 - 12*x^5 - 20*x^6 - 38*x^7 - 38*x^8 +...
A(x)*A(-x) = 1 + 5*x^2 + 15*x^4 + 36*x^6 + 87*x^8 + 320*x^10 + 1567*x^12 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A209199.

Programs

Mathematica

terms = 37; A[] = 1; Do[A[x] = 1 + x*A[x]/A[-x] + x^2*A[x]*A[-x] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Jean-François Alcover, Jan 09 2018 *)

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+x*A/subst(A,x,-x+x*O(x^n))+x^2*A*subst(A,x,-x+x*O(x^n)));polcoeff(A,n)}
for(n=0,40,print1(a(n),", "))