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Riordan array (f(x), (f(x)-1)/f(x)) where f(x) = (1 + x - sqrt(1 - 2x - 3x^2))/(2*x).
2

%I #12 Jul 24 2017 16:44:48

%S 1,1,1,1,1,1,2,2,1,1,4,4,3,1,1,9,9,6,4,1,1,21,21,15,8,5,1,1,51,51,36,

%T 22,10,6,1,1,127,127,91,54,30,12,7,1,1,323,323,232,142,75,39,14,8,1,1,

%U 835,835,603,370,205,99,49,16,9,1,1,2188,2188,1585,983

%N Riordan array (f(x), (f(x)-1)/f(x)) where f(x) = (1 + x - sqrt(1 - 2x - 3x^2))/(2*x).

%C This is essentially the reversal of the triangle in A034928, and A204849 with a duplicated first column.

%C Row sums are A005554(n+1).

%H Reinhard Zumkeller, <a href="/A247364/b247364.txt">Rows n = 0..125 of triangle, flattened</a>

%F T(n,0) = A086246(n+1), T(n+1,1) = A001006(n), T(n+2,2) = A005043(n+2).

%e Triangle begins:

%e 1

%e 1, 1

%e 1, 1, 1

%e 2, 2, 1, 1

%e 4, 4, 3, 1, 1

%e 9, 9, 6, 4, 1, 1

%e 21, 21, 15, 8, 5, 1, 1

%e 51, 51, 36, 22, 10, 6, 1, 1

%e Production matrix begins:

%e 1, 1

%e 0, 0, 1

%e 1, 1, 0, 1

%e 1, 1, 1, 0, 1

%e 1, 1, 1, 1, 0, 1

%e 1, 1, 1, 1, 1, 0, 1

%e 1, 1, 1, 1, 1, 1, 0, 1

%o (Haskell)

%o a247364 n k = a247364_tabl !! n !! k

%o a247364_row n = a247364_tabl !! n

%o a247364_tabl = [1] : (map reverse a034928_tabf)

%o -- _Reinhard Zumkeller_, Sep 20 2014

%Y Cf. A001006, A005043, A005554, A034928, A086246.

%K nonn,tabl

%O 0,7

%A _Philippe Deléham_, Sep 14 2014