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A181933
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a(n) = Sum_{k=0..n} binomial(n+k,k)*sin(Pi*(n+k)/2).
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2
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0, 1, -3, 9, -30, 106, -385, 1421, -5304, 19966, -75658, 288222, -1102790, 4234868, -16312773, 63003869, -243896960, 946066678, -3676303578, 14308370014, -55768166380, 217640082188, -850345208538, 3325907590274, -13020993588680
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1/2)*(sqrt(4*x+1)*(1+x)-3*x-1)/(sqrt(4*x+1)*(x^2+3*x+1)-4*x^2-5*x-1). - Vladimir Kruchinin, Mar 28 2016
Conjecture: +2*n*a(n) +8*n*a(n-1) +(-n+20)*a(n-2) +5*(-n+4)*a(n-3) +2*(-2*n+5)*a(n-4)=0. - R. J. Mathar, Jun 14 2016
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MATHEMATICA
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f[n_] := Sum[ Binomial[n + k, k] Sin[Pi (n + k)/2], {k, 0, n}]; Array[f, 25, 0]
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PROG
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(Maxima)
makelist(coeff(taylor(1/2*(sqrt(4*x+1)*(1+x)-3*x-1)/(sqrt(4*x+1)*(x^2+3*x+1)-4*x^2-5*x-1), x, 0, 20), x, n), n, 0, 20) /* Vladimir Kruchinin, Mar 28 2016 */
(PARI) x='x+O('x^50); concat([0], Vec((1/2)*(sqrt(4*x+1)*(1+x)-3*x-1)/(sqrt(4*x+1)*(x^2+3*x+1)-4*x^2-5*x-1))) \\ G. C. Greubel, Mar 24 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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