

A125103


Triangle read by rows: T(n,k)=binom(n,k)+2^k*binom(n,k+1) (0<=k<=n).


1



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
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OFFSET

0,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..62.


EXAMPLE

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;
...


MAPLE

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


CROSSREFS

Cf. A094374.
Sequence in context: A104698 A067066 A210219 * A171275 A284873 A107616
Adjacent sequences: A125100 A125101 A125102 * A125104 A125105 A125106


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Nov 20 2006


EXTENSIONS

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


STATUS

approved



