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A117355
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Riordan array (1/(1-x^2),x(1-2x^2)/(1-x^2)).
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1
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1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, -1, 0, 1, 0, -1, 0, -2, 0, 1, 1, 0, -2, 0, -3, 0, 1, 0, -2, 0, -2, 0, -4, 0, 1, 1, 0, -2, 0, -1, 0, -5, 0, 1, 0, -3, 0, 0, 0, 1, 0, -6, 0, 1, 1, 0, -1, 0, 3, 0, 4, 0, -7, 0, 1, 0, -4, 0, 3, 0, 6, 0, 8, 0, -8, 0, 1, 1, 0, 1, 0, 6, 0, 8, 0, 13, 0, -9, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,19
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COMMENTS
| Row sums are A077948. Diagonal sums are the aerated version of A009545 with g.f. 1/(1-2x^2+2x^4).
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FORMULA
| Number triangle T(n,k)=sum{j=0..n-k, C(j-(n-k)/2-1,j)C(k,j)(1+(-1)^(n-k))/2}
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EXAMPLE
| Triangle begins
1,
0, 1,
1, 0, 1,
0, 0, 0, 1,
1, 0, -1, 0, 1,
0, -1, 0, -2, 0, 1,
1, 0, -2, 0, -3, 0, 1,
0, -2, 0, -2, 0, -4, 0, 1
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CROSSREFS
| Sequence in context: A112761 A147310 A025886 * A086966 A140080 A065359
Adjacent sequences: A117352 A117353 A117354 * A117356 A117357 A117358
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 09 2006
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