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 A115179 Expansion of c(x*y(1-x)), c(x) the g.f. of A000108. 3
 1, 0, 1, 0, -1, 2, 0, 0, -4, 5, 0, 0, 2, -15, 14, 0, 0, 0, 15, -56, 42, 0, 0, 0, -5, 84, -210, 132, 0, 0, 0, 0, -56, 420, -792, 429, 0, 0, 0, 0, 14, -420, 1980, -3003, 1430, 0, 0, 0, 0, 0, 210, -2640, 9009, -11440, 4862, 0, 0, 0, 0, 0, -42, 1980, -15015, 40040, -43758, 16796, 0, 0, 0, 0, 0, 0, -792 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Since c(x(1-x))=1/(1-x), the row sums of this triangle are (1,1,1,...). This establishes the identity sum{k=0..n, (-1)^(n-k)*C(k)*C(k,n-k)}=1. Diagonal sums are A117437. Alternating sign version of A117434. LINKS FORMULA Number triangle T(n,k)=(-1)^(n-k)*C(k)*C(k,n-k). EXAMPLE Triangle begins .1, .0, 1, .0, -1, 2, .0, 0, -4, 5, .0, 0, 2, -15, 14, .0, 0, 0, 15, -56, 42, .0, 0, 0, -5, 84, -210, 132, .0, 0, 0, 0, -56, 420, -792, 429 CROSSREFS Sequence in context: A094295 A085969 A117434 * A131742 A257813 A278280 Adjacent sequences:  A115176 A115177 A115178 * A115180 A115181 A115182 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Mar 14 2006 STATUS approved

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)