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Search: id:A117440
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| A117440 |
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A cyclically signed version of Pascal's triangle. |
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+0
3
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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; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A009545(n+1). Diagonal sums are A117441. Inverse is A117442.
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FORMULA
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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
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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
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Adjacent sequences: A117437 A117438 A117439 this_sequence A117441 A117442 A117443
Sequence in context: A095144 A034932 A094495 this_sequence A118433 A007318 A108086
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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