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A114164 Riordan array (1/(1-2x), x(1-x)/(1-2x)^2).

%I A114164 #25 Sep 09 2024 21:40:34
%S A114164 1,2,1,4,5,1,8,18,8,1,16,56,41,11,1,32,160,170,73,14,1,64,432,620,377,
%T A114164 114,17,1,128,1120,2072,1666,704,164,20,1,256,2816,6496,6608,3649,
%U A114164 1178,223,23,1,512,6912,19392,24192,16722,7001,1826,291,26,1,1024,16640,55680,83232,69876,36365,12235,2675,368,29,1
%N A114164 Riordan array (1/(1-2x), x(1-x)/(1-2x)^2).
%C A114164 Row sums are A081567. Diagonal sums are A085810. Product of Pascal triangle A007318 and Morgan-Voyce triangle A085478.
%C A114164 Unsigned version of A123876. - _Philippe Deléham_, Oct 25 2007
%F A114164 Number triangle T(n,k) = Sum_{j=0..n} C(n, j)*C(j+k, 2k);
%F A114164 T(n,k) = Sum_{j=0..n} C(n, k+j)*C(k, k-j)*2^(n-k-j);
%F A114164 T(n,k) = Sum_{j=0..n-k} C(n+k-j, n-k-j)*C(k, j)*(-1)^j*2^(n-k-j).
%F A114164 T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Jan 17 2014
%e A114164 Triangle begins:
%e A114164    1;
%e A114164    2,   1;
%e A114164    4,   5,   1;
%e A114164    8,  18,   8,  1;
%e A114164   16,  56,  41, 11,  1;
%e A114164   32, 160, 170, 73, 14, 1;
%e A114164   ...
%Y A114164 Cf. A081567, A085810, A007318, A085478, A123876.
%Y A114164 T(2n,n) gives A026000.
%K A114164 easy,nonn,tabl
%O A114164 0,2
%A A114164 _Paul Barry_, Nov 15 2005
%E A114164 More terms from _Michel Marcus_, Sep 09 2024