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A249131 p(1,n), where the polynomial p(n,x) is defined in Comments; sum of the numbers in row n of the triangular array at A249130.

%I A249131 #7 Feb 28 2025 05:53:42
%S A249131 1,3,5,17,37,139,361,1473,4361,19091,62701,291793,1044205,5129307,
%T A249131 19748177,101817089,417787921,2250495523,9770678101,54780588561,
%U A249131 250194150581,1455367098923,6959638411705,41888448785857,208919770666777,1298019439099059
%N A249131 p(1,n), where the polynomial p(n,x) is defined in Comments; sum of the numbers in row n of the triangular array at A249130.
%C A249131 The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2*floor((n+1)/2)/f(n-1,x), where f(0,x) = 1.
%e A249131 The first 3 rows of the array at A249130:
%e A249131   1
%e A249131   2    1
%e A249131   2    2    1,
%e A249131 so that the first 3 terms of A249131 are 1,3,5.
%t A249131 z = 15; p[x_, n_] := x + 2 Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;
%t A249131 t = Table[Factor[p[x, n]], {n, 1, z}]
%t A249131 u = Numerator[t]
%t A249131 TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249130 array *)
%t A249131 u /. x -> 1  (* A249131 *)
%Y A249131 Cf. A249130.
%K A249131 nonn,easy
%O A249131 0,2
%A A249131 _Clark Kimberling_, Oct 22 2014