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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.
2
1, 3, 5, 17, 37, 139, 361, 1473, 4361, 19091, 62701, 291793, 1044205, 5129307, 19748177, 101817089, 417787921, 2250495523, 9770678101, 54780588561, 250194150581, 1455367098923, 6959638411705, 41888448785857, 208919770666777, 1298019439099059
OFFSET
0,2
COMMENTS
The polynomial p(n,x) is the numerator of the rational function given by f(n,x) = x + 2*floor(n/2))/f(n-1,x), where f(x,0) = 1.
EXAMPLE
The first 3 rows of the array at A249130:
1
2 1
2 2 1,
so that the first 3 terms of A249131 are 1,3,5.
MATHEMATICA
z = 15; p[x_, n_] := x + 2 Floor[n/2]/p[x, n - 1]; p[x_, 1] = 1;
t = Table[Factor[p[x, n]], {n, 1, z}]
u = Numerator[t]
TableForm[Table[CoefficientList[u[[n]], x], {n, 1, z}]] (* A249130 array *)
u /. x -> 1 (* A249131 *)
CROSSREFS
Cf. A249130.
Sequence in context: A305411 A019414 A350905 * A260406 A081762 A148515
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 22 2014
STATUS
approved