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Expansion of (1 + 8x - 42x^2 - 392x^3)/(1 - 99x^2 + 2450x^4).
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%I #12 Aug 03 2024 19:14:58

%S 1,8,57,400,3193,20000,176457,1000000,9646393,50000000,522673257,

%T 2500000000,28110989593,125000000000,1502438490057,6250000000000,

%U 79869486012793,312500000000000,4226104814626857,15625000000000000

%N Expansion of (1 + 8x - 42x^2 - 392x^3)/(1 - 99x^2 + 2450x^4).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,99,0,-2450).

%F G.f.: 8*(1+x)/(1-50*x^2)-7/(1-49*x^2);

%F a(n) = 99*a(n-2) - 2450*a(n-4);

%F a(n) = (4 + 2*sqrt(50)/25)*(sqrt(50))^n + (4 - 2*sqrt(50)/25)*(-sqrt(50))^n - 7^(n+1)*(1 + (-1)^n)/2;

%F a(n) = Sum_{k=0..n} binomial(floor(n/2), floor(k/2))*7^k.

%t CoefficientList[Series[(1+8x-42x^2-392x^3)/(1-99x^2+2450x^4),{x,0,20}],x] (* or *) LinearRecurrence[ {0,99,0,-2450},{1,8,57,400},20] (* _Harvey P. Dale_, Aug 03 2024 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jul 25 2004