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A142976
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a(n) = (1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)).
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5
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1, 39, 546, 5482, 47175, 373809, 2824048, 20729340, 149474205, 1065892555, 7547929806, 53215791774, 374165893891, 2626319535477, 18415017346620, 129036833755984, 903819045351033, 6329115592649775, 44313888005135290, 310239730485553170
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1+21*x-36*x^2-40*x^3) / ((1-7*x)*(4*x-1)^2*(1-x)^3). - R. J. Mathar, Sep 14 2013
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MAPLE
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MATHEMATICA
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(* First program *)
T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k - m+1)*T[n-1, k, m]];
(* Additional programs *)
CoefficientList[Series[(1 +21*x -36*x^2 -40*x^3)/((1-7*x)*(1-4*x)^2*(1-x)^3), {x, 0, 25}], x] (* Wesley Ivan Hurt, Oct 17 2017 *)
LinearRecurrence[{18, -120, 374, -567, 408, -112}, {1, 39, 546, 5482, 47175, 373809}, 40] (* Vincenzo Librandi, Oct 18 2017 *)
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PROG
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(Magma) [5/9 + n^2/2 + 7*n/6 - 4^(n+1) * (2*n/3 + 10/9) + 5*7^(n+1)/9: n in [1..25]]; // Wesley Ivan Hurt, Oct 17 2017
(Sage) [(1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)) for n in (1..30)] # G. C. Greubel, Mar 16 2022
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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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