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A038231
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Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).
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21
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1, 4, 1, 16, 8, 1, 64, 48, 12, 1, 256, 256, 96, 16, 1, 1024, 1280, 640, 160, 20, 1, 4096, 6144, 3840, 1280, 240, 24, 1, 16384, 28672, 21504, 8960, 2240, 336, 28, 1, 65536, 131072, 114688, 57344, 17920, 3584, 448, 32, 1, 262144, 589824, 589824, 344064, 129024, 32256, 5376, 576, 36, 1
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OFFSET
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0,2
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COMMENTS
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Triangle of coefficients in expansion of (4+x)^n. - N-E. Fahssi, Apr 13 2008
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LINKS
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FORMULA
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G.f. for j-th column is (x^j)/(1-4*x)^(j+1).
Convolution triangle of A000302 (powers of 4).
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EXAMPLE
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Triangle begins:
1;
4, 1;
16, 8, 1;
64, 48, 12, 1;
256, 256, 96, 16, 1;
1024, 1280, 640, 160, 20, 1;
4096, 6144, 3840, 1280, 240, 24, 1;
16384, 28672, 21504, 8960, 2240, 336, 28, 1;
65536, 131072, 114688, 57344, 17920, 3584, 448, 32, 1;
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MAPLE
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for i from 0 to 10 do seq(binomial(i, j)*4^(i-j), j = 0 .. i) od; # Zerinvary Lajos, Dec 21 2007
# Uses function PMatrix from A357368. Adds column 1, 0, 0, ... to the left.
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MATHEMATICA
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Table[4^(n-k)*Binomial[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 20 2019 *)
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PROG
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(PARI) T(n, k) = 4^(n-k)*binomial(n, k); \\ G. C. Greubel, Jul 20 2019
(Magma) [4^(n-k)*Binomial(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Jul 20 2019
(Sage) [[4^(n-k)*binomial(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jul 20 2019
(GAP) Flat(List([0..10], n-> List([0..n], k-> 4^(n-k)*Binomial(n, k) ))); # G. C. Greubel, Jul 20 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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