A173283 - OEIS

%I #15 Feb 06 2020 12:29:24

%S 1,3,8,16,32,56,96,152,240,360,536,768,1096,1520,2096,2824,3792,5000,

%T 6568,8496,10960,13960,17728,22264,27896,34624,42872,52640,64504,

%U 78464,95248,114856,138256,165448,197640,234832,278592,328920,387744,455064

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

%C (1 + 3x + 5x^2 + 7x^3 + ...) = (1 + 3x + 8x^2 + 16x^3 + ...) / (1 + 3x^2 + 8x^4 + 16x^6 + ...).

%H Alois P. Heinz, <a href="/A173283/b173283.txt">Table of n, a(n) for n = 0..10000</a>

%F Given M = triangle A152204, odd numbers shifted down twice in every column > 0.

%F A173283 = lim_{n->inf} M^n, the left-shifted vector considered as a sequence.

%F a(n) = Sum_{t=0..n/2} (2*n - 4*t + 1)*a(t). - _R. J. Mathar_, Apr 01 2010

%p 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 m = 40;

%t A[_] = 1;

%t Do[A[x_] = A[x^2] (1 + x)/(1 - x)^2 + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Feb 06 2020 *)

%Y Cf. A005408, A152204.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Feb 14 2010

%E More terms from _R. J. Mathar_, Apr 01 2010