A341768 a(n) = n * (binomial(n,2) - 2).

0, -2, -2, 3, 16, 40, 78, 133, 208, 306, 430, 583, 768, 988, 1246, 1545, 1888, 2278, 2718, 3211, 3760, 4368, 5038, 5773, 6576, 7450, 8398, 9423, 10528, 11716, 12990, 14353, 15808, 17358, 19006, 20755, 22608, 24568, 26638, 28821, 31120, 33538, 36078, 38743, 41536, 44460

Offset: 0

Author

Ilya Gutkovskiy, Feb 19 2021

Keywords

• sign
• easy

Comments

The n-th second n-gonal number.

Examples

			a(7) = A147875(7) = A000566(-7) = 133.
		

Links

• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A005449, A005564, A006002, A014105, A033954, A034856, A045944, A060354, A062728, A135705, A147875, A179986, A292551.

Programs

Mathematica

Table[n (Binomial[n, 2] - 2), {n, 0, 45}]
LinearRecurrence[{4, -6, 4, -1}, {0, -2, -2, 3}, 46]
CoefficientList[Series[-x (2 - 6 x + x^2)/(1 - x)^4, {x, 0, 45}], x]

Formula

G.f.: -x*(2 - 6*x + x^2)/(1 - x)^4.

E.g.f.: -exp(x)*x*(4 - 2*x - x^2)/2.

a(n) = n^2*(n - 1)/2 - 2*n.