A373463 Expansion of 1/((1 + x)^5 - 2*x^5).
1, -5, 15, -35, 70, -124, 190, -220, 55, 715, -2999, 8585, -20580, 43520, -81940, 134376, -176195, 118435, 279235, -1572395, 4900626, -12339900, 27139450, -53163300, 91745475, -131888749, 125584845, 66464465, -781173960, 2736565920, -7295547624, 16717081040
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (-5,-10,-10,-5,1).
Programs
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Mathematica
CoefficientList[Series[1/((1+x)^5-2x^5),{x,0,40}],x] (* or *) LinearRecurrence[{-5,-10,-10,-5,1},{1,-5,15,-35,70},40] (* Harvey P. Dale, May 25 2025 *) -
PARI
my(N=40, x='x+O('x^N)); Vec(1/((1+x)^5-2*x^5))
Formula
a(n) = -5*a(n-1) - 10*a(n-2) - 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = (-1)^n * Sum_{k=0..floor(n/5)} (-2)^k * binomial(n+4,5*k+4).