OFFSET
0,2
COMMENTS
(1 + 3x + 5x^2 + 7x^3 + ...) = (1 + 3x + 8x^2 + 16x^3 + ...) / (1 + 3x^2 + 8x^4 + 16x^6 + ...).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
Given M = triangle A152204, odd numbers shifted down twice in every column > 0.
A173283 = lim_{n->inf} M^n, the left-shifted vector considered as a sequence.
a(n) = Sum_{t=0..n/2} (2*n - 4*t + 1)*a(t). - R. J. Mathar, Apr 01 2010
MAPLE
A173283 := proc(n) option remember; if n = 0 then 1; else add(procname(l)*(2*n-4*l+1), l=0..n/2) ; end if; end proc: seq(A173283(n), n=0..60) ; # R. J. Mathar, Apr 01 2010
MATHEMATICA
m = 40;
A[_] = 1;
Do[A[x_] = A[x^2] (1 + x)/(1 - x)^2 + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Feb 06 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Feb 14 2010
EXTENSIONS
More terms from R. J. Mathar, Apr 01 2010
STATUS
approved