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A380114 Triangle read by rows: The convolution triangle of 2^n, where the convolution triangle of a sequence is defined in A357368.

%I A380114 #16 Feb 05 2025 02:17:54
%S A380114 1,0,2,0,4,4,0,8,16,8,0,16,48,48,16,0,32,128,192,128,32,0,64,320,640,
%T A380114 640,320,64,0,128,768,1920,2560,1920,768,128,0,256,1792,5376,8960,
%U A380114 8960,5376,1792,256,0,512,4096,14336,28672,35840,28672,14336,4096,512
%N A380114 Triangle read by rows: The convolution triangle of 2^n, where the convolution triangle of a sequence is defined in A357368.
%H A380114 Paolo Xausa, <a href="/A380114/b380114.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).
%F A380114 T(n, k) = 2^n * A097805(n, k). - _Werner Schulte_, Feb 04 2025
%e A380114 Triangle begins:
%e A380114   [0] [1]
%e A380114   [1] [0,   2]
%e A380114   [2] [0,   4,    4]
%e A380114   [3] [0,   8,   16,     8]
%e A380114   [4] [0,  16,   48,    48,    16]
%e A380114   [5] [0,  32,  128,   192,   128,    32]
%e A380114   [6] [0,  64,  320,   640,   640,   320,    64]
%e A380114   [7] [0, 128,  768,  1920,  2560,  1920,   768,   128]
%e A380114   [8] [0, 256, 1792,  5376,  8960,  8960,  5376,  1792,  256]
%e A380114   [9] [0, 512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512]
%t A380114 A380114[n_, k_] := 2^n*Binomial[n - 1, k - 1];
%t A380114 Table[A380114[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Feb 05 2025  *)
%o A380114 (Python) # The function ConvTriangle is defined in A357368.
%o A380114 print(ConvTriangle(10, lambda n: 2**n))
%Y A380114 Cf. A357368, A081294 (row sums), A380115 (row max), A038207 (2^(n-1)), A097805.
%K A380114 nonn,tabl
%O A380114 0,3
%A A380114 _Peter Luschny_, Feb 03 2025