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A187926 Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/2).

%I A187926 #13 Oct 31 2021 07:47:02
%S A187926 1,4,1,16,5,1,64,22,6,1,256,93,29,7,1,1024,386,130,37,8,1,4096,1586,
%T A187926 562,176,46,9,1,16384,6476,2380,794,232,56,10,1,65536,26333,9949,3473,
%U A187926 1093,299,67,11,1,262144,106762,41226,14893,4944,1471,378,79,12,1,1048576,431910,169766,63004,21778,6885,1941,470,92,13,1
%N A187926 Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/2).
%C A187926 Row sums are A000346.
%H A187926 Vincenzo Librandi, <a href="/A187926/b187926.txt">Table of n, a(n) for n = 0..5150</a>
%F A187926 a(n,k) = sum(binomial(n+i,n)*2^(n-k-i),i=0..n-k)
%F A187926 Recurrence: a(n+1,k+1) = a(n,k) + a(n,k+1) + a(n,k+2) + ... + a(n,n).
%e A187926 Triangle begins:
%e A187926 1,
%e A187926 4,1,
%e A187926 16,5,1,
%e A187926 64,22,6,1,
%e A187926 256,93,29,7,1,
%e A187926 1024,386,130,37,8,1,
%e A187926 4096,1586,562,176,46,9,1,
%e A187926 16384,6476,2380,794,232,56,10,1,
%e A187926 65536,26333,9949,3473,1093,299,67,11,1
%t A187926 Table[Sum[Binomial[n + i, n]2^(n - k - i), {i, 0, n - k}], {n, 0, 8}, {k, 0, 8}]//MatrixForm
%o A187926 (Maxima) create_list(sum(binomial(n+i,n)*2^(n-k-i),i,0,n-k),n,0,10,k,0,n);
%Y A187926 Cf. A000346
%K A187926 nonn,tabl,easy
%O A187926 0,2
%A A187926 _Emanuele Munarini_, Mar 16 2011