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Riordan array (1/(1-2*x), x*C(x)) where C(x) is the o.g.f. of Catalan numbers A000108.
2

%I #20 Sep 20 2014 09:46:24

%S 1,2,1,4,3,1,8,8,4,1,16,21,13,5,1,32,56,40,19,6,1,64,154,122,66,26,7,

%T 1,128,440,376,222,100,34,8,1,256,1309,1181,741,365,143,43,9,1,512,

%U 4048,3792,2483,1302,561,196,53,10,1,1024,12958,12446,8398,4606

%N Riordan array (1/(1-2*x), x*C(x)) where C(x) is the o.g.f. of Catalan numbers A000108.

%C Row sums are A014318.

%C Mirror image of the triangle in A201634.

%H Reinhard Zumkeller, <a href="/A247023/b247023.txt">Rows n = 0..125 of triangle, flattened</a>

%F T(n,0) = 2^n = A000079(n).

%F T(n+1,1) = A014318(n).

%e Triangle begins

%e 1

%e 2, 1

%e 4, 3, 1

%e 8, 8, 4, 1

%e 16, 21, 13, 5, 1

%e 32, 56, 40, 19, 6, 1

%e 64, 154, 122, 66, 26, 7, 1

%e Production matrix begins

%e 2, 1

%e 0, 1, 1

%e 0, 1, 1, 1

%e 0, 1, 1, 1, 1

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

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

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

%o (Haskell)

%o a247023 n k = a247023_tabl !! n !! k

%o a247023_row n = a247023_tabl !! n

%o a247023_tabl = map reverse a201634_tabl

%o -- _Reinhard Zumkeller_, Sep 20 2014

%Y Cf. A000079, A000108, A014318, A201634.

%K nonn,tabl

%O 0,2

%A _Philippe Deléham_, Sep 13 2014

%E Data corrected by _Reinhard Zumkeller_, Sep 20 2014