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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Row sums are A119332. Multiply by Pascal's triangle A007318 to get A119329. LINKS 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: A066603 A263339 A244372 * A291883 A239145 A327127 Adjacent sequences:  A119328 A119329 A119330 * A119332 A119333 A119334 KEYWORD easy,sign,tabl AUTHOR Paul Barry, May 14 2006 STATUS approved

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Last modified June 24 10:11 EDT 2021. Contains 345416 sequences. (Running on oeis4.)