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A114192 Riordan array (1/(1-2x),x/(1-2x)^2). 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 (list; table; graph; refs; listen; history; text; internal format)
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: A181854 A109822 A274292 * A114656 A294440 A346905

Adjacent sequences:  A114189 A114190 A114191 * A114193 A114194 A114195

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)