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A125103
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Triangle read by rows: T(n,k) = binomial(n,k) + 2^k*binomial(n,k+1) (0 <= k <= n).
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2
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1, 2, 1, 3, 4, 1, 4, 9, 7, 1, 5, 16, 22, 12, 1, 6, 25, 50, 50, 21, 1, 7, 36, 95, 140, 111, 38, 1, 8, 49, 161, 315, 371, 245, 71, 1, 9, 64, 252, 616, 966, 952, 540, 136, 1, 10, 81, 372, 1092, 2142, 2814, 2388, 1188, 265, 1, 11, 100, 525, 1800, 4242, 6972, 7890, 5880, 2605, 522, 1
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OFFSET
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0,2
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COMMENTS
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Row sums = A094374: (1, 3, 8, 21, 56, ...).
Binomial transform of the infinite bidiagonal matrix with (1,1,1,...) in the main diagonal and (1,2,4,8,...) in the subdiagonal.
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LINKS
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EXAMPLE
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First few rows of the triangle are
1;
2, 1;
3, 4, 1;
4, 9, 7, 1;
5, 16, 22, 12, 1;
6, 25, 50, 50, 21, 1;
7, 36, 95, 140, 111, 38, 1;
...
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MAPLE
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T:=(n, k)->binomial(n, k)+2^k*binomial(n, k+1): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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MATHEMATICA
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Table[Binomial[n, k]+2^k Binomial[n, k+1], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Nov 30 2019 *)
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PROG
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(PARI) T(n, k) = binomial(n, k) + 2^k*binomial(n, k+1);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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