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A155050
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A symmetric Catalan based triangle.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 2, 5, 5, 2, 1, 1, 1, 1, 2, 5, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 42, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 42, 42, 14, 5, 2, 1, 1, 1, 1, 2, 5, 14, 42, 132, 42, 14, 5, 2, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Central coefficients are A000108. Row sums are A155051.
Image under Riordan array ((1+x)/(1-x),x)^{-1} is A155052.
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FORMULA
| Number triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(ct(j+1)-ct(j))} where ct(n):=if(n=0,0,A000108(n-1)).
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EXAMPLE
| Triangle begins
1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 1, 2, 1, 1,
1, 1, 2, 2, 1, 1,
1, 1, 2, 5, 2, 1, 1,
1, 1, 2, 5, 5, 2, 1, 1,
1, 1, 2, 5, 14, 5, 2, 1, 1,
1, 1, 2, 5, 14, 14, 5, 2, 1, 1,
1, 1, 2, 5, 14, 42, 14, 5, 2, 1, 1
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CROSSREFS
| Sequence in context: A139040 A139147 A055801 * A140356 A119963 A057790
Adjacent sequences: A155047 A155048 A155049 * A155051 A155052 A155053
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 19 2009
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