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A173283 A(x) satisfies A005408(x) = A(x)/A(x^2), A005408 = odd numbers.

%I A173283 #15 Feb 06 2020 12:29:24
%S A173283 1,3,8,16,32,56,96,152,240,360,536,768,1096,1520,2096,2824,3792,5000,
%T A173283 6568,8496,10960,13960,17728,22264,27896,34624,42872,52640,64504,
%U A173283 78464,95248,114856,138256,165448,197640,234832,278592,328920,387744,455064
%N A173283 A(x) satisfies A005408(x) = A(x)/A(x^2), A005408 = odd numbers.
%C A173283 (1 + 3x + 5x^2 + 7x^3 + ...) = (1 + 3x + 8x^2 + 16x^3 + ...) / (1 + 3x^2 + 8x^4 + 16x^6 + ...).
%H A173283 Alois P. Heinz, <a href="/A173283/b173283.txt">Table of n, a(n) for n = 0..10000</a>
%F A173283 Given M = triangle A152204, odd numbers shifted down twice in every column > 0.
%F A173283 A173283 = lim_{n->inf} M^n, the left-shifted vector considered as a sequence.
%F A173283 a(n) = Sum_{t=0..n/2} (2*n - 4*t + 1)*a(t). - _R. J. Mathar_, Apr 01 2010
%p A173283 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
%t A173283 m = 40;
%t A173283 A[_] = 1;
%t A173283 Do[A[x_] = A[x^2] (1 + x)/(1 - x)^2 + O[x]^m // Normal, {m}];
%t A173283 CoefficientList[A[x], x] (* _Jean-François Alcover_, Feb 06 2020 *)
%Y A173283 Cf. A005408, A152204.
%K A173283 nonn
%O A173283 0,2
%A A173283 _Gary W. Adamson_, Feb 14 2010
%E A173283 More terms from _R. J. Mathar_, Apr 01 2010