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 A352988 Matrix inverse of triangle A352650. 1
 1, 0, 1, -1, -1, 1, 0, -2, -2, 1, 0, 0, -3, -3, 1, 0, 0, 0, -4, -4, 1, 0, 0, 0, 0, -5, -5, 1, 0, 0, 0, 0, 0, -6, -6, 1, 0, 0, 0, 0, 0, 0, -7, -7, 1, 0, 0, 0, 0, 0, 0, 0, -8, -8, 1, 0, 0, 0, 0, 0, 0, 0, 0, -9, -9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Table of n, a(n) for n=0..77. FORMULA T(n,n) = 1 for n >= 0, and T(n,n-1) = 1 - n for n > 0, and T(n,n-2) = 1 - n for n > 1, and T(n,k) = 0 if n < 0 or k < 0 or n < k or n > k+2. G.f.: Sum_{n>=0, k=0..n} T(n,k) * x^k * t^n = (1 + t) * (1 - (1 + x) * t) / (1 - x * t)^2. Alt. row sums equal (-1)^n for n >= 0. Matrix product with A094587 yields A097806. EXAMPLE The triangle T(n,k) for 0 <= k <= n starts: n\k : 0 1 2 3 4 5 6 7 8 9 ====================================================== 0 : 1 1 : 0 1 2 : -1 -1 1 3 : 0 -2 -2 1 4 : 0 0 -3 -3 1 5 : 0 0 0 -4 -4 1 6 : 0 0 0 0 -5 -5 1 7 : 0 0 0 0 0 -6 -6 1 8 : 0 0 0 0 0 0 -7 -7 1 9 : 0 0 0 0 0 0 0 -8 -8 1 etc. CROSSREFS Cf. A094587, A097806, A352650. Sequence in context: A258277 A122865 A246656 * A334493 A074080 A359440 Adjacent sequences: A352985 A352986 A352987 * A352989 A352990 A352991 KEYWORD sign,easy,tabl AUTHOR Werner Schulte, Apr 13 2022 STATUS approved

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Last modified February 21 09:51 EST 2024. Contains 370228 sequences. (Running on oeis4.)