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A360322
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a(n) = Sum_{k=0..n} (-5)^(n-k) * binomial(n-1,n-k) * binomial(2*k,k).
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4
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1, 2, -4, 10, -30, 102, -376, 1462, -5900, 24470, -103644, 446382, -1948854, 8605290, -38362200, 172423770, -780496110, 3554991270, -16281079900, 74927379550, -346328465930, 1607078948690, -7483861047480, 34963419415650, -163825013554400, 769694347677002
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: sqrt( (1+5*x)/(1+x) ).
n*a(n) = 2*(-3*n+4)*a(n-1) - 5*(n-2)*a(n-2).
Sum_{i=0..n} Sum_{j=0..i} (-1/5)^i * a(j) * a(i-j) = (1/5)^n.
a(n) = 2 * (-1)^(n+1) * A007317(n) for n > 0.
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PROG
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(PARI) a(n) = sum(k=0, n, (-5)^(n-k)*binomial(n-1, n-k)*binomial(2*k, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1+5*x)/(1+x)))
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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