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A113214
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Riordan array (1+2x,x(1+x)).
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1
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1, 2, 1, 0, 3, 1, 0, 2, 4, 1, 0, 0, 5, 5, 1, 0, 0, 2, 9, 6, 1, 0, 0, 0, 7, 14, 7, 1, 0, 0, 0, 2, 16, 20, 8, 1, 0, 0, 0, 0, 9, 30, 27, 9, 1, 0, 0, 0, 0, 2, 25, 50, 35, 10, 1, 0, 0, 0, 0, 0, 11, 55, 77, 44, 11, 1, 0, 0, 0, 0, 0, 2, 36, 105, 112, 54, 12, 1, 0, 0, 0, 0, 0, 0, 13, 91, 182, 156, 65, 13, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums are Lucas numbers A000204. Diagonal sums are A007307(n+1). Inverse is (-1)^(n-k)A092392(n,k). Product with Pascal triangle (1/(1-x),x/(1-x)) is A111125.
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FORMULA
| T(n, k)=C(k, n-k)+2C(k, n-k-1); T(n, k)=sum{j=0..n, (-1)^(n-j)*C(n, j)C(j+k, 2k)(2j+1)/(2k+1)}.
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EXAMPLE
| Triangle begins
1;
2,1;
0,3,1;
0,2,4,1;
0,0,5,5,1;
0,0,2,9,6,1;
0,0,0,7,14,7,1;
0,0,0,2,16,20,8,1;
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CROSSREFS
| Sequence in context: A202452 A127013 A117362 * A168016 A029323 A194849
Adjacent sequences: A113211 A113212 A113213 * A113215 A113216 A113217
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 18 2005
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