A117665 n times the n-th n-gonal number.

0, 2, 6, 24, 80, 210, 462, 896, 1584, 2610, 4070, 6072, 8736, 12194, 16590, 22080, 28832, 37026, 46854, 58520, 72240, 88242, 106766, 128064, 152400, 180050, 211302, 246456, 285824, 329730, 378510, 432512, 492096, 557634, 629510, 708120, 793872

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n (n + 1) (n^2 - 3 n + 4)/2. - corrected by Eric Rowland, Aug 15 2017

From Chai Wah Wu, Jul 29 2016: (Start)

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

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

Mathematica

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

Prog

(PARI) a(n)=n*(n+1)*(n^2-3*n+4)/2 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Cf. A060354.

Sequence in context: A263747 A002526 A324373 * A068777 A275206 A095110

Adjacent sequences: A117662 A117663 A117664 * A117666 A117667 A117668

Keyword

nonn,easy

Author

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

Status

approved