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

1,1

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).

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)

Prog

(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

Crossrefs

Cf. A286718.

Sequence in context: A278009 A233333 A271793 * A004415 A096949 A093974

Adjacent sequences: A024210 A024211 A024212 * A024214 A024215 A024216

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved