A024212 2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.
4, 39, 159, 445, 1005, 1974, 3514, 5814, 9090, 13585, 19569, 27339, 37219, 49560, 64740, 83164, 105264, 131499, 162355, 198345, 240009, 287914, 342654, 404850, 475150, 554229, 642789, 741559, 851295, 972780, 1106824, 1254264, 1415964, 1592815, 1785735
Offset: 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 (5,-10,10,-5,1).
Programs
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Magma
[n*(n+1)*(9*n^2+9*n-2)/8: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011
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Mathematica
Table[n(n+1)(9n^2+9n-2)/8,{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{4,39,159,445,1005},40] (* Harvey P. Dale, Oct 16 2023 *)
Formula
a(n) = n*(n+1)*(9*n^2+9*n-2)/8.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Clark Kimberling, Aug 18 2012
G.f.: (4 + 19*x + 4*x^2)/(1 - x)^5. - Clark Kimberling, Aug 18 2012
From Wolfdieter Lang, Jul 30 2017: (Start)
E.g.f.: exp(x)*x*(32+124*x+72*x^2+9*x^3)/8 = exp(x)*x*(2 + x)*(16 + 54*x + 9*x^2)/8.
a(n) = A286718(n+1, n-1), n >= 1. (End)