A380114 Triangle read by rows: The convolution triangle of 2^n, where the convolution triangle of a sequence is defined in A357368.
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, 640, 320, 64, 0, 128, 768, 1920, 2560, 1920, 768, 128, 0, 256, 1792, 5376, 8960, 8960, 5376, 1792, 256, 0, 512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512
Offset: 0
Examples
Triangle begins: [0] [1] [1] [0, 2] [2] [0, 4, 4] [3] [0, 8, 16, 8] [4] [0, 16, 48, 48, 16] [5] [0, 32, 128, 192, 128, 32] [6] [0, 64, 320, 640, 640, 320, 64] [7] [0, 128, 768, 1920, 2560, 1920, 768, 128] [8] [0, 256, 1792, 5376, 8960, 8960, 5376, 1792, 256] [9] [0, 512, 4096, 14336, 28672, 35840, 28672, 14336, 4096, 512]
Links
- Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
Programs
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Mathematica
A380114[n_, k_] := 2^n*Binomial[n - 1, k - 1]; Table[A380114[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Feb 05 2025 *)
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Python
# The function ConvTriangle is defined in A357368. print(ConvTriangle(10, lambda n: 2**n))
Formula
T(n, k) = 2^n * A097805(n, k). - Werner Schulte, Feb 04 2025