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Search: id:A154556
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| A154556 |
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Exponential Riordan array [exp(-x), x(1+x/2)] |
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+0
1
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| 1, -1, 1, 1, -1, 1, -1, 0, 0, 1, 1, 2, -3, 2, 1, -1, -5, 5, -5, 5, 1, 1, 9, 0, -5, 0, 9, 1, -1, -14, -21, 35, -35, 21, 14, 1, 1, 20, 70, -56, 35, -56, 70, 20, 1, -1, -27, -162, -42, 189, -189, 42, 162, 27
(list; table; graph; listen)
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OFFSET
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0,12
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COMMENT
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Row sums are double factorials A001147 (aerated). Product A007318*A154556 is A122848.
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FORMULA
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Triangle T(n,k)=(n!/k!)*sum{j=0..k, (-1)^(n-k)*C(k,j)*(-1/2)^j/(n-k-j)!};
T(n,k)=sum{j=0..n, (-1)^(n-j)*C(n,j)*C(j,k)*k!/((2k-j)!*2^(j-k))};
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EXAMPLE
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Triangle begins
1,
-1, 1,
1, -1, 1,
-1, 0, 0, 1,
1, 2, -3, 2, 1,
-1, -5, 5, -5, 5, 1,
1, 9, 0, -5, 0, 9, 1,
-1, -14, -21, 35, -35, 21, 14, 1,
1, 20, 70, -56, 35, -56, 70, 20, 1,
-1, -27, -162, -42, 189, -189, 42, 162, 27, 1,
1, 35, 315, 510, -735, 693, -735, 510, 315, 35, 1
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CROSSREFS
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Sequence in context: A017838 A058294 A082868 this_sequence A126626 A137927 A084311
Adjacent sequences: A154553 A154554 A154555 this_sequence A154557 A154558 A154559
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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), Jan 11 2009
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