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(PARI) Vec(1 / ((1 - x)^2*(1 - 2*x + 2*x^2)) + O(x^50)) \\ Colin Barker, Aug 04 2017
(PARI) {a(n) = sum(k=0, n\2, (-1)^k*binomial(n+3, 2*k+3))} \\ Seiichi Manyama, Apr 07 2019
From Seiichi Manyama, Apr 07 2019: (Start)
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n+3,2*k+3).
a(n) = Sum_{i=0..n} Sum_{j=0..n-i} (-1)^j * binomial(i+1,j+1) * binomial(n-i+1,j+1). (End)
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Colin Barker, <a href="/A279230/b279230.txt">Table of n, a(n) for n = 0..1000</a>
<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-7,6,-2).
a(n) = (3 - (1-i)^(1+n) - (1+i)^(1+n) + n) where i=sqrt(-1). - Colin Barker, Aug 04 2017
Vec(1 / ((1 - x)^2*(1 - 2*x + 2*x^2)) + O(x^50)) \\ Colin Barker, Aug 04 2017
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