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Search: id:A133815
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| A133815 |
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Square array of Hankel transforms of C(n+k,floor((n+k)/2)), read by anti-diagonals. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, -1, 2, 1, 1, -1, 3, 3, 1, 1, 1, 4, -6, 6, 1, 1, 1, 5, -10, 20, 10, 1, 1, -1, 6, 15, 50, -50, 20, 1, 1, -1, 7, 21, 105, -175, 175, 35, 1, 1, 1, 8, -28, 196, 490, 980, -490, 70, 1, 1, 1, 9, -36, 336, 1176, 4116, -4116, 1764, 126, 1
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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T(n+1,k) is the Hankel transform of C(n+k,floor((n+k)/2)). Even indexed columns count tilings of hexagons: A002415 (<2,n,2>),A047819 (<3,n,3>), A047835 (<4,n,4>) etc.
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FORMULA
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T(n,k)=if(mod(k,2)=0, Product{j=0..(k-2)/2,C(n+k/2+j,k/2)/C(k/2+j,k/2)},(cos(pi*n/2)+sin(pi*n/2)) *Product{j,0..(k-3)/2, C(n+(k+1)/2+j,(k+1)/2)/C((k+1)/2+j,(k+1)/2)})
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EXAMPLE
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Array begins
1, 1, 1, 1, 1, 1;
1, 1, 2, 3, 6, 10;
1, -1, 3, -6, 20, -50;
1, -1, 4, -10, 50, -175;
1, 1, 5, 15, 105, 490;
1, 1, 6, 21, 196, 1176
As a number triangle, T(n-k,k) gives
1,
1, 1,
1, 1, 1,
1, -1, 2, 1,
1, -1, 3, 3, 1,
1, 1, 4, -6, 6, 1,
1, 1, 5, -10, 20, 10, 1,
1, -1, 6, 15, 50, -50, 20, 1
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CROSSREFS
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Cf. A120247, A103905.
Sequence in context: A047120 A096751 A099233 this_sequence A130580 A110541 A079115
Adjacent sequences: A133812 A133813 A133814 this_sequence A133816 A133817 A133818
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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), Sep 24 2007
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