A216713 G.f.: A(x) = 1 + x*A(x)^2 / ( A(w*x)*A(w^2*x) ), where w = exp(2*Pi*I/3).

1, 1, 3, 12, 27, 105, 420, 1242, 5295, 22395, 72738, 323268, 1410684, 4806675, 21881721, 97371786, 341608239, 1579726122, 7123796790, 25489388367, 119184247992, 542664427242, 1969440159591, 9284827569117, 42584603672868, 156213604844883, 741154831030785

Offset: 0

Author

Paul D. Hanna, Sep 14 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 27*x^4 + 105*x^5 + 420*x^6 +...
Related expansions:
A(x)^2 = 1 + 2*x + 7*x^2 + 30*x^3 + 87*x^4 + 336*x^5 + 1356*x^6 +...
A(x)^3 = 1 + 3*x + 12*x^2 + 55*x^3 + 189*x^4 + 756*x^5 + 3132*x^6 +...
Let w = exp(2*Pi*I/3), then A(x) = 1 + x*A(x)^3/(A(x)*A(w*x)*A(w^2*x)) where
A(x)*A(w*x)*A(w^2*x) = 1 + 28*x^3 + 1134*x^6 + 61857*x^9 + 3929121*x^12 + 272388420*x^15 + 19981576476*x^18 + 1524888581787*x^21 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A143339, A212527, A216712, A216681.

Programs

PARI

{a(n)=local(A=1+x*O(x^n));for(i=1,n+1,A=1+x*A^3*exp(-3*sum(m=1,n\3,x^(3*m)*polcoeff(log(A),3*m))+x*O(x^n)));polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))