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A117440
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A cyclically signed version of Pascal's triangle.
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2
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1, 1, 1, -1, 2, 1, -1, -3, 3, 1, 1, -4, -6, 4, 1, 1, 5, -10, -10, 5, 1, -1, 6, 15, -20, -15, 6, 1, -1, -7, 21, 35, -35, -21, 7, 1, 1, -8, -28, 56, 70, -56, -28, 8, 1, 1, 9, -36, -84, 126, 126, -84, -36, 9, 1, -1, 10, 45, -120, -210, 252, 210, -120, -45, 10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are A009545(n+1). Diagonal sums are A117441. Inverse is A117442.
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FORMULA
| Column k has e.g.f. (x^k/k!)*(cos(x)+sin(x)); Number triangle T(n,k)=C(n,k)*(cos(pi*(n-k)/2)+sin(pi*(n-k)/2);
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EXAMPLE
| Triangle begins
1,
1, 1,
-1, 2, 1,
-1, -3, 3, 1,
1, -4, -6, 4, 1,
1, 5, -10, -10, 5, 1,
-1, 6, 15, -20, -15, 6, 1,
-1, -7, 21, 35, -35, -21, 7, 1
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CROSSREFS
| Sequence in context: A094495 A154926 * A118433 A007318 A108086 A130595
Adjacent sequences: A117437 A117438 A117439 * A117441 A117442 A117443
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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