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A097114
Expansion of (1 + 8x - 42x^2 - 392x^3)/(1 - 99x^2 + 2450x^4).
0
1, 8, 57, 400, 3193, 20000, 176457, 1000000, 9646393, 50000000, 522673257, 2500000000, 28110989593, 125000000000, 1502438490057, 6250000000000, 79869486012793, 312500000000000, 4226104814626857, 15625000000000000
OFFSET
0,2
FORMULA
G.f.: 8*(1+x)/(1-50*x^2)-7/(1-49*x^2);
a(n) = 99*a(n-2) - 2450*a(n-4);
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;
a(n) = Sum_{k=0..n} binomial(floor(n/2), floor(k/2))*7^k.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A297369 A023000 A331792 * A022038 A277671 A015453
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 25 2004
STATUS
approved