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A081039
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4th binomial transform of (1,3,0,0,0,0,0,.....).
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5
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1, 7, 40, 208, 1024, 4864, 22528, 102400, 458752, 2031616, 8912896, 38797312, 167772160, 721420288, 3087007744, 13153337344, 55834574848, 236223201280, 996432412672, 4191888080896, 17592186044416, 73667279060992
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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) = 8*a(n-1) -16*a(n-2) with n>1, a(0)=1, a(1)=7.
a(n) = (3*n+4)*4^(n-1).
a(n) = sum( k=0..n, (k+1)*3^k*binomial(n, k) ).
G.f.: (1-x)/(1-4*x)^2.
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MATHEMATICA
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CoefficientList[Series[(1 - x)/(1 - 4 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{8, -16}, {1, 7}, 30] (* Harvey P. Dale, Dec 13 2015 *)
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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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