A124929 - OEIS

%I #18 Sep 08 2022 08:45:28

%S 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,

%T 465,378,127,1,21,147,525,1085,1323,889,255,1,24,196,840,2170,3528,

%U 3556,2040,511,1,27,252,1260,3906,7938,10668,9180,4599,1023

%N Triangle read by rows: T(n,k) = (2^k-1)*binomial(n-1,k-1) (1<=k<=n).

%C Row sums give A027649.

%H G. C. Greubel, <a href="/A124929/b124929.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%e First few rows of the triangle are:

%e   1;

%e   1,  3;

%e   1,  6,  7;

%e   1,  9, 21,  15;

%e   1, 12, 42,  60,  31;

%e   1, 15, 70, 150, 155, 63;

%e ...

%p 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

%t Table[(2^k -1)*Binomial[n-1, k-1], {n,12}, {k,n}]//Flatten (* _G. C. Greubel_, Jun 08 2017 *)

%o (PARI) for(n=1,12, for(k=1,n, print1((2^k -1)*binomial(n-1,k-1), ", "))) \\ _G. C. Greubel_, Jun 08 2017

%o (Magma) [(2^k -1)*Binomial(n-1,k-1): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Nov 19 2019

%o (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

%o (GAP) Flat(List([1..12], n-> List([1..n], k-> (2^k -1)*Binomial(n-1,k-1) ))); # _G. C. Greubel_, Nov 19 2019

%Y Cf. A027649.

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_, Nov 12 2006

%E Edited by _N. J. A. Sloane_, Nov 29 2006