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A119331
Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)*2^j}}.
2
1, 0, 1, 0, -1, 1, 0, 1, -2, 1, 0, -1, 5, -3, 1, 0, 1, -8, 12, -4, 1, 0, -1, 11, -28, 22, -5, 1, 0, 1, -14, 51, -68, 35, -6, 1, 0, -1, 17, -81, 159, -135, 51, -7, 1, 0, 1, -20, 118, -312, 390, -236, 70, -8, 1, 0, -1, 23, -162, 544, -926, 816, -378, 92, -9, 1
OFFSET
0,9
COMMENTS
Row sums are A119332. Multiply by Pascal's triangle A007318 to get A119329.
FORMULA
Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,2j)*2^j*x^(2j)}
EXAMPLE
Triangle begins
1,
0, 1,
0, -1, 1,
0, 1, -2, 1,
0, -1, 5, -3, 1,
0, 1, -8, 12, -4, 1,
0, -1, 11, -28, 22, -5, 1,
0, 1, -14, 51, -68, 35, -6, 1,
0, -1, 17, -81, 159, -135, 51, -7, 1,
0, 1, -20, 118, -312, 390, -236, 70, -8, 1,
0, -1, 23, -162, 544, -926, 816, -378, 92, -9, 1
CROSSREFS
Sequence in context: A263339 A244372 A370773 * A351641 A291883 A361957
KEYWORD
easy,sign,tabl
AUTHOR
Paul Barry, May 14 2006
STATUS
approved