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Search: id:A113187
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| 1, -3, 1, 10, -5, 1, -35, 21, -7, 1, 126, -84, 36, -9, 1, -462, 330, -165, 55, -11, 1, 1716, -1287, 715, -286, 78, -13, 1, -6435, 5005, -3003, 1365, -455, 105, -15, 1, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1, 352716, -293930, 203490
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are (-1)^n*A000984. Diagonal sums are (-1)^n*A014301(n+1). An interesting factorization is (1/sqrt(1+4x)),(sqrt(1+4x)-1)/2)(1/(1+x),x/(1+x)).
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FORMULA
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Riordan array ((sqrt(1+4x)-1)/(2x*sqrt(1+4x)), (1+2x-sqrt(1+4x))/(2x)); T(n, k)=(-1)^(n-k)*C(2n+1, n+k+1); T(n, k)=sum{j=0..n, (-1)^(n-k)*C(2n-j, n-j)C(j, k)}.
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EXAMPLE
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Triangle begins
1;
-3, 1;
10, -5, 1;
-35, 21, -7, 1;
126, -84, 36, -9, 1;
-462, 330, -165, 55, -11, 1;
1716,-1287, 715, -286, 78,-13, 1;
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CROSSREFS
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Sequence in context: A078817 A091042 A111418 this_sequence A057967 A132964 A134283
Adjacent sequences: A113184 A113185 A113186 this_sequence A113188 A113189 A113190
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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), Oct 17 2005
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