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

1,3

Comments

Row sums give A027649.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Example

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;
...

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

Mathematica

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

Prog

(PARI) for(n=1, 12, for(k=1, n, print1((2^k -1)*binomial(n-1, k-1), ", "))) \\ G. C. Greubel, Jun 08 2017
(Magma) [(2^k -1)*Binomial(n-1, k-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 19 2019
(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
(GAP) Flat(List([1..12], n-> List([1..n], k-> (2^k -1)*Binomial(n-1, k-1) ))); # G. C. Greubel, Nov 19 2019

Crossrefs

Cf. A027649.

Sequence in context: A291217 A198614 A239385 * A208766 A259454 A209696

Adjacent sequences: A124926 A124927 A124928 * A124930 A124931 A124932

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 12 2006

Extensions

Edited by N. J. A. Sloane, Nov 29 2006

Status

approved