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Triangle read by rows related to A000984, central binomial coefficients
3

%I #10 Apr 08 2013 05:19:52

%S 1,1,1,1,4,1,1,12,6,1,1,33,27,8,1,1,88,108,44,10,1,1,232,405,208,65,

%T 12,1,1,609,1459,908,350,90,14,1

%N Triangle read by rows related to A000984, central binomial coefficients

%F T(n,k) = A191314(2*n,k).

%F Take finite differences of even numbered columns of the A205573 array from the top -> down.

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 1, 4, 1;

%e 1, 12, 6, 1;

%e 1, 33, 27, 8, 1;

%e 1, 88, 108, 44, 10, 1;

%e 1, 232, 405, 208, 65, 12, 1;

%e 1, 609, 1459, 908, 350, 90, 14, 1;

%e ...

%e Row 2 = (1, 4, 1) = row 4 of triangle A191314.

%e Row 3 = (1, 12, 6, 1) = finite differences of column 6 of the array shown in A205573: (1, 13, 19, 20)

%Y Cf. A000984 (row sums), A001405, A191314, A205573, A205945 (companion).

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Feb 01 2012