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A142976 a(n) = (1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)).

%I A142976 #18 Sep 08 2022 08:45:37
%S A142976 1,39,546,5482,47175,373809,2824048,20729340,149474205,1065892555,
%T A142976 7547929806,53215791774,374165893891,2626319535477,18415017346620,
%U A142976 129036833755984,903819045351033,6329115592649775,44313888005135290,310239730485553170
%N A142976 a(n) = (1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)).
%H A142976 Vincenzo Librandi, <a href="/A142976/b142976.txt">Table of n, a(n) for n = 1..1000</a>
%H A142976 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-120,374,-567,408,-112).
%F A142976 a(n) = A142458(n+2,n).
%F A142976 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
%p A142976 A142976:=n->5/9 + n^2/2 + 7*n/6 - 4^(n+1) * (2*n/3 + 10/9) + 5*7^(n+1)/9: seq(A142976(n), n=1..25); # _Wesley Ivan Hurt_, Oct 17 2017
%t A142976 (* First program *)
%t A142976 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]];
%t A142976 A142976[n_]:= T[n+2,n,3];
%t A142976 Table[A142976[n], {n,30}] (* modified by _G. C. Greubel_, Mar 16 2022 *)
%t A142976 (* Additional programs *)
%t A142976 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 *)
%t A142976 LinearRecurrence[{18,-120,374,-567,408,-112}, {1,39,546,5482,47175,373809}, 40] (* _Vincenzo Librandi_, Oct 18 2017 *)
%o A142976 (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
%o A142976 (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
%Y A142976 Cf. A142458, A144380, A144381, A144414.
%K A142976 nonn,easy
%O A142976 1,2
%A A142976 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 01 2008