A085456 Sum_{i=0..n} Sum_{j=0..i} a(j) * a(i-j) = (-7)^n.
1, -4, 20, -116, 708, -4452, 28532, -185300, 1215268, -8030404, 53381844, -356577588, 2391430020, -16092704292, 108605848116, -734783381652, 4982063186916, -33844621986180, 230306722637204, -1569571734301172, 10711405584991300, -73188920628617956, 500643475619050740
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
CoefficientList[Series[Sqrt[(1-x)/(1+7 x)], {x, 0, 30}], x] -
PARI
a(n) = sum(k=0, n, (-2)^k*binomial(n-1, n-k)*binomial(2*k, k)); \\ Seiichi Manyama, Feb 03 2023
Formula
G.f.: A(x)=Sqrt((1-x)/(1+7x)).
From Seiichi Manyama, Feb 03 2023: (Start)
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)