OFFSET
1,3
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)
EXAMPLE
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)) +...
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 13 2010
STATUS
approved