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 A131085 Triangle T(n,k) (n>=0, 0<=k<=n-1) read by rows, A007318 * A129686. 2
 1, 1, 1, 0, 2, 1, -2, 2, 3, 1, -5, 0, 5, 4, 1, -9, -5, 5, 9, 5, 1, -14, -14, 0, 14, 14, 6, 1, -20, -28, -14, 14, 28, 20, 7, 1, -27, -48, -42, 0, 42, 48, 27, 8, 1, -35, -75, -90, -42, 42, 90, 75, 35, 9, 1, -44, -110, -165, -132, 0, 132, 165, 110, 44, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = n. A131085 * A000012 = A074909 starting (1, 2, 1, 3, 3, ...) instead of (1, 1, 2, 1, 3, 3, ...). LINKS FORMULA Binomial transform of A129686 signed with (1, 1, 1, ...) in the main diagonal and (-1, -1, -1, ...) in the subsubdiagonal. T(n,m) = T(n-1,m-1) + T(n-1,m). - Yuchun Ji, Dec 17 2018 T(2*k,k-1) = 0 for k > 0. - Yuchun Ji, Dec 20 2018 Comparing this triangle with the Catalan triangle A009766 one can see many similarities. For example, T(k+j,k) = A009766(k+1,j) for j < k+2. - Yuchun Ji, Dec 23 2018 [Edited by N. J. A. Sloane, Feb 11 2019] EXAMPLE First few rows of the triangle are:    1;    1,  1;    0,  2, 1;   -2,  2, 3, 1;   -5,  0, 5, 4, 1;   -9, -5, 5, 9, 5, 1; -14, -14, 0, 14, 14, 6, 1; -20, -28, -14, 14, 28, 20, 7, 1; -27, -48, -42, 0, 42, 48, 27, 8, 1; -35, -75, -90, -42, 42, 90, 75, 35, 9, 1;    ... PROG (PARI) tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t129686 = matrix(nn, nn, n, k, (k<=n)*((-1)^((n-k)\2)*((k==n) || (-1)*(k==(n-2))))); t131085 = t007318*t129686; for (n = 1, nn, for (k = 1, n, print1(t131085[n, k], ", "); ); ); } \\ Michel Marcus, Feb 12 2014 CROSSREFS Cf. A007318, A009766, A097808, A112466, A214292, A112467, A129686, A131084. Sequence in context: A133755 A336470 A070104 * A303280 A318717 A331887 Adjacent sequences:  A131082 A131083 A131084 * A131086 A131087 A131088 KEYWORD sign,tabl AUTHOR Gary W. Adamson, Jun 14 2007 EXTENSIONS Missing comma corrected by Naruto Canada, Aug 26 2007 More terms from Michel Marcus, Feb 12 2014 Offset changed by N. J. A. Sloane, Feb 11 2019 STATUS approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)