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 A137289 Triangle read by rows: T(n,k) = (-1)^(n-k)*(C(k+n-1,n-k)-2*C(k+n-1,n-k-1)) for n>=0 and 0<=k<=n. 2
 -1, 2, 1, -2, 0, 1, 2, -3, -2, 1, -2, 8, 0, -4, 1, 2, -15, 10, 7, -6, 1, -2, 24, -35, 0, 18, -8, 1, 2, -35, 84, -42, -30, 33, -10, 1, -2, 48, -168, 168, 0, -88, 52, -12, 1, 2, -63, 300, -462, 198, 143, -182, 75, -14, 1, -2, 80, -495, 1056, -858, 0, 455, -320, 102, -16, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: "Expansion of certain polynomials; see formula." LINKS FORMULA B(x, 0) = -1, B(x, 2) = x^2 + 2, B(x, 3) = x^3 + x, B(x, 4) = x^4 - 2, and B(x, n) = x*B(x, n - 1) - B(x, n - 2) for n>=2, expand B(sqrt(x), 2*n). EXAMPLE {-1}, {2, 1}, {-2, 0, 1}, {2, -3, -2, 1}, {-2, 8, 0, -4, 1}, {2, -15, 10, 7, -6, 1}, {-2, 24, -35, 0, 18, -8, 1}, {2, -35, 84, -42, -30, 33, -10, 1}, {-2, 48, -168, 168,0, -88, 52, -12, 1}, {2, -63, 300, -462, 198, 143, -182, 75, -14,1}, {-2, 80, -495, 1056, -858, 0, 455, -320, 102, -16, 1} MAPLE T := (n, k) -> (-1)^(n-k)*(binomial(k+n-1, n-k)-2*binomial(k+n-1, n-k-1)): seq(seq(T(n, k), k=0..n), n=0..10); # Peter Luschny, May 15 2016 MATHEMATICA B[x, 0] = -1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 4] = -2 + x^4; B[ x, 3] = x + x^3; B[x_, n_] := B[x, n] = x*B[x, n - 1] - B[x, n - 2]; a = Table[CoefficientList[B[x, n] /. x -> Sqrt[y], y], {n, 0, 20, 2}]; Flatten[a] CROSSREFS Cf. A135929, A138034. Sequence in context: A114004 A049986 A218797 * A211359 A211357 A238416 Adjacent sequences:  A137286 A137287 A137288 * A137290 A137291 A137292 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Mar 14 2008 EXTENSIONS Edited by N. J. A. Sloane, Jan 05 2009 Edited by Joerg Arndt, Nov 15 2014 New name and changed a(1) to -1 by Peter Luschny, May 15 2016 STATUS approved

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Last modified January 23 21:17 EST 2019. Contains 319404 sequences. (Running on oeis4.)