A117665 - OEIS

%I #11 Oct 21 2022 21:27:38

%S 0,2,6,24,80,210,462,896,1584,2610,4070,6072,8736,12194,16590,22080,

%T 28832,37026,46854,58520,72240,88242,106766,128064,152400,180050,

%U 211302,246456,285824,329730,378510,432512,492096,557634,629510,708120,793872

%N n times the n-th n-gonal number.

%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 (n + 1) (n^2 - 3 n + 4)/2. - corrected by _Eric Rowland_, Aug 15 2017

%F From _Chai Wah Wu_, Jul 29 2016: (Start)

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.

%F G.f.: 2*x*(1 - 2*x + 7*x^2)/(1 - x)^5. (End)

%t LinearRecurrence[{5,-10,10,-5,1},{0,2,6,24,80},50] (* _Harvey P. Dale_, Jan 02 2020 *)

%o (PARI) a(n)=n*(n+1)*(n^2-3*n+4)/2 \\ _Charles R Greathouse IV_, Oct 21 2022

%Y Cf. A060354.

%K nonn,easy

%O 0,2

%A Luc Stevens (lms022(AT)yahoo.com), Apr 11 2006