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A049016
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Expansion of 1/((1-x)^5 - x^5).
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15
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1, 5, 15, 35, 70, 127, 220, 385, 715, 1430, 3004, 6385, 13380, 27370, 54740, 107883, 211585, 416405, 826045, 1652090, 3321891, 6690150, 13455325, 26985675, 53971350, 107746282, 214978335, 429124630, 857417220, 1714834440, 3431847189
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/((1-x)^5-x^5) = 1/( (1-2*x)*(1-3*x+4*x^2-2*x^3+x^4) ).
Binomial transform of expansion of (1+x)^4/(1-x^5), or (1, 4, 6, 4, 1, 1, 4, 6, 4, 1, ...). - Paul Barry, Mar 19 2004
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + 2*a(n-5). - Paul Curtz, May 24 2008
G.f.: -1/( x^5 - 1 + 5*x/Q(0) ) where Q(k) = 1 + k*(x+1) + 5*x - x*(k+1)*(k+6)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Mar 15 2013
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^5-x^5), {x, 0, 30}], x] (* or *) LinearRecurrence[ {5, -10, 10, -5, 2}, {1, 5, 15, 35, 70}, 40] (* Harvey P. Dale, Jan 20 2014 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/((1-x)^5-x^5) )); // G. C. Greubel, Apr 11 2023
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x)^5-x^5) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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