A213281 G.f. satisfies: A(x) = 1 + x/A(-x)^3.

1, 1, 3, -3, -35, 48, 693, -1046, -16635, 26328, 442396, -720327, -12541509, 20810208, 371430414, -624691212, -11356013899, 19293440712, 355703260500, -609103135196, -11355804637164, 19568456886336, 368147199241021, -637674031240302, -12087185276792061

Offset: 0

Author

Paul D. Hanna, Jun 08 2012

Keywords

• sign

Examples

			G.f.: A(x) = 1 + x + 3*x^2 - 3*x^3 - 35*x^4 + 48*x^5 + 693*x^6 - 1046*x^7 +...
where
1/A(-x) = 1 + x - 2*x^2 - 8*x^3 + 30*x^4 + 143*x^5 - 638*x^6 - 3272*x^7 +...
x/A(-x)^3 = x + 3*x^2 - 3*x^3 - 35*x^4 + 48*x^5 + 693*x^6 - 1046*x^7 +...
A(x)^3 = 1 + 3*x + 12*x^2 + 10*x^3 - 87*x^4 - 102*x^5 + 1632*x^6 + 1974*x^7 +...
The g.f. G(x) of A213282 begins:
G(x) = 1 + x + 6*x^2 + 36*x^3 + 236*x^4 + 1656*x^5 + 12192*x^6 + 92960*x^7 +...
where G(x) = A(x*G(x)^3) and G(x/A(x)^3) = A(x);
also, G(x) = F(x/(1-x)^3) where F(x) = 1 + x*F(x)^3 is g.f. of A001764:
G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A213282, A213252, A213335; A001764.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+x/subst(A^3,x,-x+x*O(x^n)));polcoeff(A,n)}
for(n=0,40,print1(a(n),", "))

Formula

G.f. satisfies: A(x) = G(x/A(x)^3) where G(x) = A(x*G(x)^3) is the g.f. of A213282.

G.f. satisfies: A(x) = ( x/Series_Reversion( x*F(x/(1-x)^3)^3 ) )^(1/3) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764.

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