A124929 Triangle read by rows: T(n,k) = (2^k-1)*binomial(n-1,k-1) (1<=k<=n).
1, 1, 3, 1, 6, 7, 1, 9, 21, 15, 1, 12, 42, 60, 31, 1, 15, 70, 150, 155, 63, 1, 18, 105, 300, 465, 378, 127, 1, 21, 147, 525, 1085, 1323, 889, 255, 1, 24, 196, 840, 2170, 3528, 3556, 2040, 511, 1, 27, 252, 1260, 3906, 7938, 10668, 9180, 4599, 1023
Offset: 1
Examples
First few rows of the triangle are: 1; 1, 3; 1, 6, 7; 1, 9, 21, 15; 1, 12, 42, 60, 31; 1, 15, 70, 150, 155, 63; ...
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Crossrefs
Cf. A027649.
Programs
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GAP
Flat(List([1..12], n-> List([1..n], k-> (2^k -1)*Binomial(n-1,k-1) ))); # G. C. Greubel, Nov 19 2019
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Magma
[(2^k -1)*Binomial(n-1,k-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 19 2019
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Maple
T:=(n,k)->(2^k-1)*binomial(n-1,k-1): for n from 1 to 11 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form
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Mathematica
Table[(2^k -1)*Binomial[n-1, k-1], {n,12}, {k,n}]//Flatten (* G. C. Greubel, Jun 08 2017 *) -
PARI
for(n=1,12, for(k=1,n, print1((2^k -1)*binomial(n-1,k-1), ", "))) \\ G. C. Greubel, Jun 08 2017
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Sage
[[(2^k -1)*binomial(n-1,k-1) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Nov 19 2019
Extensions
Edited by N. J. A. Sloane, Nov 29 2006
Comments