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A024212
2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.
10
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
1,1
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)
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 *)
PROG
(Magma) [n*(n+1)*(9*n^2+9*n-2)/8: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011
CROSSREFS
Sequence in context: A297736 A286359 A201740 * A006408 A112460 A296594
KEYWORD
nonn,easy
STATUS
approved