A114192 Riordan array (1/(1-2x),x/(1-2x)^2).

1, 2, 1, 4, 6, 1, 8, 24, 10, 1, 16, 80, 60, 14, 1, 32, 240, 280, 112, 18, 1, 64, 672, 1120, 672, 180, 22, 1, 128, 1792, 4032, 3360, 1320, 264, 26, 1, 256, 4608, 13440, 14784, 7920, 2288, 364, 30, 1, 512, 11520, 42240, 59136, 41184, 16016, 3640, 480, 34, 1

Offset

0,2

Comments

Factors as (1/(1-x),x/(1-x))*(1/(1-x),x*(1+x)/(1-x)^2) or A007318 times A114188. Also (1/(1-2*x),x/(1-2*x))*(1,x*(1+2*x)). Inverse is A114193. Row sums are A007583. Diagonal sums are A007051.

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = sum{j=0..n, C(k, j)*C(n, k+j)}*2^(n-k).

T(n,k) = 2^(n-k)*binomial(n+k,2k) = 2^(n-k)*A085478(n,k). - Philippe Deléham, May 05 2006

T(n,k) = A013609(n+k, n-k). - Johannes W. Meijer, Sep 05 2013

T(n,k) = 4*T(n-1,k) + T(n-1,k-1) - 4*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 17 2014

Example

Triangle begins
1;
2, 1;
4, 6, 1;
8, 24, 10, 1;
16, 80, 60, 14, 1;
32, 240, 280, 112, 18, 1;

Crossrefs

Sequence in context: A372396 A274292 A359670 * A114656 A294440 A346905

Adjacent sequences: A114189 A114190 A114191 * A114193 A114194 A114195

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 16 2005

Status

approved