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 A137277 Triangle of the coefficients [x^k] P_n(x) of the polynomials P_n(x) = 1/n * sum(j=0..floor(n/2), (-1)^j * binomial(n,j) * (n-4*j) * x^(n-2*j) ). 2
 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, -6, 0, 0, 0, 1, 0, -6, 0, -1, 0, 1, 20, 0, -5, 0, -2, 0, 1, 0, 25, 0, -3, 0, -3, 0, 1, -70, 0, 28, 0, 0, 0, -4, 0, 1, 0, -98, 0, 28, 0, 4, 0, -5, 0, 1, 252, 0, -126, 0, 24, 0, 9, 0, -6, 0, 1, 0, 378, 0, -150, 0, 15, 0, 15, 0, -7, 0, 1, -924, 0, 528, 0, -165, 0, 0, 0, 22, 0, -8, 0, 1, 0, -1452 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The first four P_n(x) are the same as in A137276. Row sums are 1, 1, 3, 2, -5, -6, 14, 20, -45, -70, 154, a signed variant of A047074. LINKS FORMULA P(0,n)=1. P_n(x) = 1/n*sum(j=0..floor(n/2), (-1)^j*binomial(n,j)*(n-4*j)*x^(n-2*j)). EXAMPLE {1}, = 1 {0, 1}, = x {2, 0, 1}, = 2+x^2 {0, 1, 0, 1}, = x+x^3 {-6, 0, 0, 0, 1}, = -6+x^4 {0, -6, 0, -1, 0, 1}, {20, 0, -5, 0, -2, 0, 1}, {0, 25, 0, -3,0, -3, 0, 1}, {-70, 0, 28, 0, 0, 0, -4, 0, 1}, {0, -98, 0, 28, 0,4, 0, -5, 0, 1}, {252, 0, -126, 0, 24, 0, 9, 0, -6, 0, 1} MAPLE A137277 := proc(n, k) if n = 0 then 1; else add( (-1)^j*binomial(n, j)*(n-4*j)*x^(n-2*j), j=0..n/2)/n ; coeftayl(%, x=0, k) ; fi; end: seq( seq(A137277(n, k), k=0..n), n=0..15) ; MATHEMATICA B[x_, n_] = If[n > 0, Sum[(-1)^p*Binomial[n, p]*(n - 4*p)*x^(n - 2*p)/ n, {p, 0, Floor[n/2]}], 1]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a] CROSSREFS Cf. A138034. Sequence in context: A137276 A287234 A140581 * A039975 A016253 A286998 Adjacent sequences:  A137274 A137275 A137276 * A137278 A137279 A137280 KEYWORD sign,easy,tabl AUTHOR Roger L. Bagula, Mar 13 2008 EXTENSIONS Edited by the Associate Editors of the OEIS, Aug 27 2009 STATUS approved

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Last modified June 19 06:47 EDT 2019. Contains 324218 sequences. (Running on oeis4.)