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A049016 Expansion of 1/((1-x)^5-x^5). 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2)

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A000750, A078789.

Sequence in context: A140227 A264925 * A139761 A275935 A137360 A195760

Adjacent sequences:  A049013 A049014 A049015 * A049017 A049018 A049019

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 21 15:58 EST 2018. Contains 299414 sequences. (Running on oeis4.)