A375373 Expansion of 1/( (1 + x)^2 * (1 - x^2*(1 + x)^2) ).
1, -2, 4, -4, 6, -4, 9, -4, 16, 0, 28, 16, 57, 58, 132, 172, 322, 476, 817, 1272, 2112, 3360, 5496, 8832, 14353, 23158, 37540, 60668, 98238, 158876, 257145, 415988, 673168, 1089120, 1762324, 2851408, 4613769, 7465138, 12078948, 19544044, 31623034, 51167036
Offset: 0
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (-2,0,4,6,4,1).
Programs
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Mathematica
CoefficientList[Series[1/((1+x)^2(1-x^2(1+x)^2)),{x,0,50}],x] (* or *) LinearRecurrence[{-2,0,4,6,4,1},{1,-2,4,-4,6,-4},50] (* Harvey P. Dale, Dec 11 2024 *) -
PARI
my(N=50, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x^2*(1+x)^2))) -
PARI
a(n) = sum(k=0, n\2, binomial(2*k-2, n-2*k));
Formula
a(n) = -2*a(n-1) + 4*a(n-3) + 6*a(n-4) + 4*a(n-5) + a(n-6).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k-2,n-2*k).