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 A174295 Matrix inverse of A174294. 6
 1, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, 1, 1, -2, -1, 1, 0, 1, -3, 2, 0, -2, 2, 0, 1, 6, -7, -3, 3, -3, 3, 0, 1, -15, 14, 3, -10, 7, -4, 4, 0, 1, 36, -37, -12, 19, -19, 12, -5, 5, 0, 1, -91, 90, 24, -54, 42, -30, 18, -6, 6, 0, 1, 232, -233, -67, 127, -115, 73, -43, 25, -7, 7 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,17 COMMENTS First column is a signed version of A099323 with an additional leading 1. First 5 rows as in A054525. LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA Sum_{k=0..n} T(n, k) = A000007(n). T(n, 0) = A174297(n). EXAMPLE Table begins: n\k|...0...1...2...3...4...5...6...7...8...9..10 ---|-------------------------------------------- 0..|...1 1..|..-1...1 2..|..-1...0...1 3..|...0..-1...0...1 4..|..-1...0...0...0...1 5..|...1..-2..-1...1...0...1 6..|..-3...2...0..-2...2...0...1 7..|...6..-7..-3...3..-3...3...0...1 8..|.-15..14...3.-10...7..-4...4...0...1 9..|..36.-37.-12..19.-19..12..-5...5...0...1 10.|.-91..90..24.-54..42.-30..18..-6...6...0...1 MATHEMATICA t[n_, k_]:= t[n, k]= If[k<0 || k>n, 0, If[k==0 || k==n, 1, If[k==1, Mod[n, 2], t[n-1, k-1] +t[n-2, k-1] -t[n-1, k] -t[n-2, k] ]]]; (* t = A174294 *) M:= With[{m=30}, Table[t[n, k], {n, 0, m}, {k, 0, m}]]; T:= Inverse[M]; Table[T[[n+1, k+1]], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 25 2021 *) CROSSREFS Cf. A000007 (row sums), A054525, A099323, A112467, A112468, A174294, A174296, A174297. Sequence in context: A105806 A129501 A129353 * A158511 A092921 A191607 Adjacent sequences: A174292 A174293 A174294 * A174296 A174297 A174298 KEYWORD sign,tabl AUTHOR Mats Granvik, Mar 15 2010 STATUS approved

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Last modified December 1 04:40 EST 2023. Contains 367468 sequences. (Running on oeis4.)