A179489 G.f.: A(x) = x/(1 - (1-3x)*A( x/(1-3x) )).

1, 1, 2, 8, 44, 288, 2172, 18516, 175352, 1819868, 20491844, 248417128, 3221797252, 44464876996, 650076797232, 10028658649668, 162695157490644, 2767333692834768, 49221196196394252, 913310582666986596

Offset: 1

Author

Paul D. Hanna, Aug 13 2010

Keywords

• nonn

Examples

			G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 44*x^5 + 288*x^6 + ...
A(x) = x + x*A(x) + x*A(x)*A(x/(1-3x)) + x*A(x)*A(x/(1-3x))*A(x/(1-6x)) + x*A(x)*A(x/(1-3x))*A(x/(1-6x))*A(x/(1-9x)) +...
		

Crossrefs

Cf. variants: A074664, A179488.

Programs

PARI

{a(n)=local(A=x+x^2);for(i=1,n,A=x/(1-(1-3*x)*subst(A,x,x/(1-3*x+x^2*O(x^n)))));polcoeff(A,n)}

Formula

G.f.: A(x) = x/(1 - (1-3x)*x/(1-3x - (1-6x)*x/(1-6x - (1-9x)*x/(1-9x - (1-12x)*x/(1-12x - ... (continued fraction).

From Gary W. Adamson, Jul 22 2011: (Start)

a(n) = the upper left term in M^(n-1), M = an infinite square production matrix with the series 3*n-2 as the main diagonal:

1, 1, 0, 0, 0, ...

1, 4, 1, 0, 0, ...

1, 1, 7, 1, 0, ...

1, 1, 1,10, 0, ...

... (End)