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A081041
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6th binomial transform of (1,5,0,0,0,0,0,0,...).
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3
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1, 11, 96, 756, 5616, 40176, 279936, 1912896, 12877056, 85660416, 564350976, 3688436736, 23944605696, 154551545856, 992612745216, 6347497291776, 40435908673536, 256721001578496, 1624959306694656, 10257555623510016
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 12*a(n-1) - 36*a(n-2) for n>1, a(0)=1, a(1)=9.
a(n) = (5*n+6)*6^(n-1).
a(n) = Sum_{k=0..n} (k+1)*5^k*binomial(n, k).
G.f.: (1-x)/(1-6x)^2.
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MATHEMATICA
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CoefficientList[Series[(1 - x)/(1 - 6 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{12, -36}, {1, 11}, 20] (* Harvey P. Dale, Mar 04 2019 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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