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Search: id:A117435
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| A117435 |
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Triangle related to exp(x)cos(2x). |
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+0
3
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| 1, 0, 1, -4, 0, 1, 0, -12, 0, 1, 16, 0, -24, 0, 1, 0, 80, 0, -40, 0, 1, -64, 0, 240, 0, -60, 0, 1, 0, -448, 0, 560, 0, -84, 0, 1, 256, 0, -1792, 0, 1120, 0, -112, 0, 1, 0, 2304, 0, -5376, 0, 2016, 0, -144, 0, 1, -1024, 0, 11520, 0, -13440, 0, 3360, 0, -180, 0, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums are A006495 (with e.g.f. exp(x)cos(2x)). Inverse is A117436. Diagonal sums are (1,0,-3,0,5,0,-7,...). Diagonals correspond to rows of A117438.
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FORMULA
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Number triangle whose k-th column has e.g.f. (x^k/k!)*cos(2x); T(n,k)=C(n,k)*(-4)^((n-k)/2)*(1+(-1)^(n-k))/2.
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EXAMPLE
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Triangle begins
1,
0, 1,
-4, 0, 1,
0, -12, 0, 1,
16, 0, -24, 0, 1,
0, 80, 0, -40, 0, 1,
-64, 0, 240, 0, -60, 0, 1
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CROSSREFS
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Cf. A117411.
Sequence in context: A147312 A019974 A046781 this_sequence A117436 A166318 A166317
Adjacent sequences: A117432 A117433 A117434 this_sequence A117436 A117437 A117438
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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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