A375163 Expansion of 1/((1 + x)^7 - 2*x^7).
1, -7, 28, -84, 210, -462, 924, -1714, 2975, -4795, 6888, -7616, 1428, 27132, -116276, 352632, -919303, 2180101, -4815188, 10010980, -19650050, 36268478, -62075384, 95196038, -118778345, 73332329, 207719344, -1138579904, 3670243032, -9852434200, 23858720872
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (-7,-21,-35,-35,-21,-7,1).
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(1/((1+x)^7-2*x^7))
Formula
a(n) = -7*a(n-1) - 21*a(n-2) - 35*a(n-3) - 35*a(n-4) - 21*a(n-5) - 7*a(n-6) + a(n-7).
a(n) = (-1)^n * Sum_{k=0..floor(n/7)} (-2)^k * binomial(n+6,7*k+6).