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A375291
Expansion of (1 - x + x^4)/((1 - x + x^4)^2 + 4*x^5).
0
1, 1, 1, 1, 0, -5, -14, -27, -43, -50, -20, 91, 342, 784, 1380, 1861, 1519, -1025, -7877, -21302, -41829, -64128, -70003, -19381, 155984, 544288, 1208731, 2073244, 2706380, 2003100, -2136215, -12820099, -33219215, -63581579, -94886444, -98351925, -12445158
OFFSET
0,6
FORMULA
a(n) = 2*a(n-1) - a(n-2) - 2*a(n-4) - 2*a(n-5) - a(n-8).
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(2*n-6*k,2*k).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^4)/((1-x+x^4)^2+4*x^5))
(PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(2*n-6*k, 2*k));
CROSSREFS
Cf. A375289.
Sequence in context: A185233 A065351 A002503 * A014106 A110325 A331775
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 10 2024
STATUS
approved