A024392 a(n) = 3rd elementary symmetric function of the first n+2 positive integers congruent to 2 mod 3.

80, 806, 4040, 14155, 39655, 95200, 204036, 400830, 734910, 1273910, 2107820, 3353441, 5159245, 7710640, 11235640, 16010940, 22368396, 30701910, 41474720, 55227095, 72584435, 94265776, 121092700, 153998650, 194038650, 242399430

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Magma

[n*(n+1)*(n+2)*(3*n+7)*(9*n^2+33*n+22)/48: n in [1..40]]; // Vincenzo Librandi, Jul 07 2019

Mathematica

Table[n (n + 1) (n + 2) (3 n + 7) (9 n^2 + 33 n + 22) / 48, {n, 1, 50}] (* Vincenzo Librandi, Jul 07 2019 *)

Formula

a(n) = n*(n+1)*(n+2)*(3*n+7)*(9*n^2+33*n+22)/48.

G.f.: -x*(80+246*x+78*x^2+x^3) / (x-1)^7 . - R. J. Mathar, Oct 08 2011