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Sum of terms in n-th row of A081491.
4

%I #17 Sep 08 2022 08:45:09

%S 1,5,18,54,135,291,560,988,1629,2545,3806,5490,7683,10479,13980,18296,

%T 23545,29853,37354,46190,56511,68475,82248,98004,115925,136201,159030,

%U 184618,213179,244935,280116,318960,361713,408629,459970,516006,577015

%N Sum of terms in n-th row of A081491.

%C For odd n a(n) is a multiple of n and a(n)/n is the middle term of the corresponding row.

%H Harvey P. Dale, <a href="/A081492/b081492.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = n*(2*n^3 - 6*n^2 + 13*n - 3)/6.

%F G.f.: x*(1+x)*(1-x+4*x^2)/(1-x)^5. - _Colin Barker_, Jul 28 2012

%F E.g.f.: x*(6 +9*x +6*x^2 +2*x^3)/6. - _G. C. Greubel_, Aug 13 2019

%p seq(n*(2*(n-1)^3+7*n-1)/6, n=1..40); # _G. C. Greubel_, Aug 13 2019

%t LinearRecurrence[{5,-10,10,-5,1},{1,5,18,54,135},40] (* _Harvey P. Dale_, Jul 01 2018 *)

%o (PARI) vector(40, n, n*(2*(n-1)^3+7*n-1)/6) \\ _G. C. Greubel_, Aug 13 2019

%o (Magma) [n*(2*(n-1)^3+7*n-1)/6: n in [1..40]]; // _G. C. Greubel_, Aug 13 2019

%o (Sage) [n*(2*(n-1)^3+7*n-1)/6 for n in (1..40)] # _G. C. Greubel_, Aug 13 2019

%o (GAP) List([1..40], n-> n*(2*(n-1)^3+7*n-1)/6); # _G. C. Greubel_, Aug 13 2019

%Y Cf. A002522, A005408, A081489, A081490, A081491.

%K nonn,easy

%O 1,2

%A _Amarnath Murthy_, Mar 25 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003.

%E Formula corrected by _Colin Barker_, Jul 28 2012