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A089513
Third column of triangle A089504.
6
1, 90, 6156, 387720, 23705136, 1432922400, 86230132416, 5179923146880, 310942155338496, 18660051727004160, 1119687641441381376, 67183287394552842240, 4031045937469026349056, 241863924899255181189120
OFFSET
0,2
COMMENTS
Convolution of A089507 with powers of 60.
FORMULA
G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)*(1-5*4*3*x)).
a(n)=A089504(n+3, 3), n>=0.
a(n)= (50*(5*4*3)^n - 24*(4*3*2)^n + (3*2*1)^n)/27 = (6^n)*(5*10^(n+1) - 3*2^(2*n+3) + 1)/27.
MATHEMATICA
CoefficientList[Series[1/(1-90 x+1944 x^2-8640 x^3), {x, 0, 20}], x] (* or *) LinearRecurrence[{90, -1944, 8640}, {1, 90, 6156}, 20] (* Harvey P. Dale, Jul 07 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Dec 01 2003
STATUS
approved