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G.f.: 1/((1-x)*(1-x^2))^5.
5

%I #9 Oct 01 2023 12:50:59

%S 1,5,20,60,160,376,820,1660,3190,5830,10252,17380,28600,45760,71500,

%T 109252,163735,240955,348920,497640,700128,972400,1334840,1812200,

%U 2435420,3241628,4276520,5594360,7261040,9354080,11966504,15206840

%N G.f.: 1/((1-x)*(1-x^2))^5.

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (5, -5, -15, 35, 1, -65, 45, 45, -65, 1, 35, -15, -5, 5, -1).

%F a(2*k) = binomial(k + 7, 7)*(4*k^2 + 23*k + 18)/18 = A059601(k); a(2*k + 1) = binomial(k + 7, 7)*(4*k^2 + 41*k + 90)/18 = A059602(k), k >= 0.

%t CoefficientList[Series[1/((1-x)(1-x^2))^5,{x,0,35}],x] (* _Harvey P. Dale_, Apr 02 2011 *)

%Y Cf. A008619, A006918, A038163.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.