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A375372
Expansion of 1/( (1 + x) * (1 - x^2*(1 + x)^2) ).
2
1, -1, 2, 0, 2, 2, 5, 5, 12, 16, 28, 44, 73, 115, 190, 304, 494, 798, 1293, 2089, 3384, 5472, 8856, 14328, 23185, 37511, 60698, 98208, 158906, 257114, 416021, 673133, 1089156, 1762288, 2851444, 4613732, 7465177, 12078907, 19544086, 31622992, 51167078, 82790070
OFFSET
0,3
FORMULA
a(n) = -a(n-1) + a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k-1,n-2*k).
a(n) = A375373(n) + A375373(n-1).
2*a(n) = 2*(-1)^n + A000045(n) + A057078(n+1). - R. J. Mathar, Aug 14 2024
PROG
(PARI) my(N=50, x='x+O('x^N)); Vec(1/((1+x)*(1-x^2*(1+x)^2)))
(PARI) a(n) = sum(k=0, n\2, binomial(2*k-1, n-2*k));
CROSSREFS
Sequence in context: A301823 A301999 A171936 * A071055 A183034 A354101
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Aug 13 2024
STATUS
approved