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A085456
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Sum_{i=0..n} Sum_{j=0..i} a(j) * a(i-j) = (-7)^n.
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3
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1, -4, 20, -116, 708, -4452, 28532, -185300, 1215268, -8030404, 53381844, -356577588, 2391430020, -16092704292, 108605848116, -734783381652, 4982063186916, -33844621986180, 230306722637204, -1569571734301172, 10711405584991300, -73188920628617956, 500643475619050740
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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.: A(x)=Sqrt((1-x)/(1+7x)).
a(n) = Sum_{k=0..n} (-2)^k * binomial(n-1,n-k) * binomial(2*k,k).
n*a(n) = -2*(3*n-1)*a(n-1) + 7*(n-2)*a(n-2). (End)
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MATHEMATICA
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CoefficientList[Series[Sqrt[(1-x)/(1+7 x)], {x, 0, 30}], x]
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PROG
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(PARI) a(n) = sum(k=0, n, (-2)^k*binomial(n-1, n-k)*binomial(2*k, k)); \\ Seiichi Manyama, Feb 03 2023
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jul 01 2003
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STATUS
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approved
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