A024213 a(n) = 3rd elementary symmetric function of first n+2 positive integers congruent to 1 mod 3.

28, 418, 2485, 9605, 28700, 72128, 159978, 322770, 604560, 1066450, 1790503, 2884063, 4484480, 6764240, 9936500, 14261028, 20050548, 27677490, 37581145, 50275225, 66355828, 86509808, 111523550, 142292150, 179829000, 225275778

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Wolfdieter Lang, On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles, arXiv:1708.01421 [math.NT], August 2017.
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A286718.

Programs

Magma

[n*(n+1)*(n+2)*(3*n+5)*(9*n^2+21*n-2)/48: n in [1..30]]; // Vincenzo Librandi, Oct 10 2011

Formula

a(n) = n*(n+1)*(n+2)*(3n+5)*(9n^2+21*n-2)/48.

G.f. -x*(28+222*x+147*x^2+8*x^3) / (x-1)^7 . - R. J. Mathar, Oct 08 2011

From Wolfdieter Lang, Jul 30 2017: (Start)

E.g.f.: x*exp(x)*(1344 + 8688*x + 10520*x^2 + 4122*x^3 + 594*x^4 + 27*x^5)/48.

a(n) = A286718(n+2, n-1), n >= 1. (End)