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 A144389 Triangle T(n,k) = n*binomial(n - 1, k) - (-1)^(n - k)*binomial(n, k), T(0,0) = 1, read by rows, 0 <= k <= n. 1
 -1, 2, -1, 1, 4, -1, 4, 3, 6, -1, 3, 16, 6, 8, -1, 6, 15, 40, 10, 10, -1, 5, 36, 45, 80, 15, 12, -1, 8, 35, 126, 105, 140, 21, 14, -1, 7, 64, 140, 336, 210, 224, 28, 16, -1, 10, 63, 288, 420, 756, 378, 336, 36, 18, -1, 9, 100, 315, 960, 1050, 1512, 630, 480, 45, 20, -1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA T(n,k) = [x^k] (n*(x + 1)^(n - 1) - (x - 1)^n). Sum_{k=0..n} T(n,k) = A001787(n), n >= 1. EXAMPLE Triangle begins:   -1;    2,  -1;    1,   4,  -1;    4,   3,   6,  -1;    3,  16,   6,   8,   -1;    6,  15,  40,  10,   10,   -1;    5,  36,  45,  80,   15,   12,  -1;    8,  35, 126, 105,  140,   21,  14,  -1;    7,  64, 140, 336,  210,  224,  28,  16, -1;   10,  63, 288, 420,  756,  378, 336,  36, 18, -1;    9, 100, 315, 960, 1050, 1512, 630, 480, 45, 20, -1;   ... MATHEMATICA p[x_, n_] = -(x - 1)^n + n*(x + 1)^(n - 1); Table[CoefficientList[p[x, n], x], {n, 0, 10}] // Flatten PROG (Maxima) create_list(n*binomial(n - 1, k) - (-1)^(n - k)*binomial(n, k), n , 0, 15, k, 0, n); /* Franck Maminirina Ramaharo, Jan 25 2019 */ CROSSREFS Cf. A001787, A007318, A130595, A144388, A216973. Sequence in context: A328649 A281422 A344529 * A136321 A112987 A125138 Adjacent sequences:  A144386 A144387 A144388 * A144390 A144391 A144392 KEYWORD sign,easy,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 01 2008 STATUS approved

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Last modified January 27 18:40 EST 2022. Contains 350611 sequences. (Running on oeis4.)