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A049016
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Expansion of 1/((1-x)^5-x^5).
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12
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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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Seiichi Manyama, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2)
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FORMULA
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G.f.: 1/((1-x)^5-x^5) = 1 / ( (1-2*x)*(x^4-2*x^3+4*x^2-3*x+1) ).
a(10n+3) = A078789(5n+3), a(10n+5) = A078789(5n+4).
a(n) = (-1)^n A000750(n).
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) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(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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CROSSREFS
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Cf. A000750, A078789.
Sequence in context: A342213 A140227 A264925 * A139761 A275935 A137360
Adjacent sequences: A049013 A049014 A049015 * A049017 A049018 A049019
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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