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 A136255 Triangle T(n,k) read by rows: T(n,k) = (k+1) * A137276(n,k+1). 1
 1, 0, 2, 1, 0, 3, 0, 0, 0, 4, -3, 0, -3, 0, 5, 0, -6, 0, -8, 0, 6, 5, 0, -6, 0, -15, 0, 7, 0, 16, 0, 0, 0, -24, 0, 8, -7, 0, 30, 0, 15, 0, -35, 0, 9, 0, -30, 0, 40, 0, 42, 0, -48, 0, 10, 9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums are 1, 2, 4, 4, -1, -8, -9, 0, 12, 14, 1, ... with g.f. x*(1+3*x^2) / (x^2-x+1)^2. LINKS FORMULA T(n,k) = (k+1) * A137276(n,k+1) . EXAMPLE Triangle starts: {1}, {0, 2}, {1, 0, 3}, {0, 0, 0, 4}, {-3, 0, -3, 0, 5}, {0, -6, 0, -8, 0, 6}, {5, 0, -6, 0, -15, 0, 7}, {0, 16, 0, 0, 0, -24, 0, 8}, {-7, 0, 30, 0, 15, 0, -35, 0, 9}, {0, -30, 0, 40, 0,42, 0, -48, 0, 10}, {9, 0, -75, 0, 35, 0, 84, 0, -63, 0, 11}, ... MAPLE B := proc(n, x) if n = 0 then 1; else add( (-1)^j*binomial(n-j, j)*(n-4*j)/(n-j)*x^(n-2*j), j=0..n/2) ; fi; end: A136255 := proc(n, k) diff( B(n, x), x) ; coeftayl(%, x=0, k) ; end: seq( seq(A136255(n, k), k=0..n-1), n=1..15) ; MATHEMATICA B[x, 0] = 1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 3] = x + x^3; B[x, 4] = -2 + x^4; B[x_, n_] := B[x, n] = x*B[x, n-1] - B[x, n-2]; P[x_, n_] := D[B[x, n + 1], x]; Flatten @ Table[CoefficientList[P[x, n], x], {n, 0, 10}] CROSSREFS Cf. A138034, A135929, A135936, A137276, A137277, A137289. Sequence in context: A266832 A307772 A225203 * A194812 A305320 A159813 Adjacent sequences:  A136252 A136253 A136254 * A136256 A136257 A136258 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Mar 17 2008 EXTENSIONS Edited by the Associate Editors of the OEIS, Aug 27 2009 Edited by and new name from Joerg Arndt, May 15 2016 STATUS approved

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Last modified August 21 05:48 EDT 2019. Contains 326162 sequences. (Running on oeis4.)