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A114195 Riordan array (1/(1-3x),x(1-x)/(1-3x)^2). 2
1, 3, 1, 9, 8, 1, 27, 45, 13, 1, 81, 216, 106, 18, 1, 243, 945, 690, 192, 23, 1, 729, 3888, 3915, 1574, 303, 28, 1, 2187, 15309, 20223, 10941, 2993, 439, 33, 1, 6561, 58320, 97524, 67788, 24598, 5072, 600, 38, 1, 19683, 216513, 446148, 385560, 177498 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A082685. Diagonal sums are A114196.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

T(n, k)=sum{j=0..n, C(n, j)C(j+k, 2k)2^(j-k)}; T(n, k)=sum{j=0..n-k, C(k, j)C(n+k-j, 2k)(-1)^j*3^(n-k-j)}.

T(n,k) = 6*T(n-1,k) + T(n-1,k-1) - 9*T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = 3, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 18 2014

EXAMPLE

Triangle begins

1;

3, 1;

9, 8, 1;

27, 45, 13, 1;

81, 216, 106, 18, 1;

243, 945, 690, 192, 23, 1;

CROSSREFS

Sequence in context: A136320 A201840 A088640 * A185948 A016601 A193031

Adjacent sequences:  A114192 A114193 A114194 * A114196 A114197 A114198

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)