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

Author

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

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A060354.

Programs

Mathematica

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

PARI

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

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)