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A024178
a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3)/(2+3+...+n+3)).
1
2, 11, 29, 61, 115, 196, 312, 474, 690, 971, 1331, 1781, 2335, 3010, 3820, 4782, 5916, 7239, 8771, 10535, 12551, 14842, 17434, 20350, 23616, 27261, 31311, 35795, 40745, 46190, 52162, 58696, 65824, 73581, 82005, 91131, 100997, 111644, 123110, 135436
OFFSET
1,1
FORMULA
G.f.: x*(x^3 - 3x^2 + 3x + 2)/((1-x^3)*(1-x)^4).
a(n) = floor((1/24)*n*(n+1)*(n^2 + 9*n + 22)). - Ivan Neretin, May 21 2018
MATHEMATICA
s[n_] := 1 + Range[n + 2]
Table[Floor[SymmetricPolynomial[3, s[n]]/SymmetricPolynomial[1, s[n]]], {n, 1,
46}] (* Clark Kimberling, Sep 23 2016 *)
LinearRecurrence[{4, -6, 5, -5, 6, -4, 1}, {2, 11, 29, 61, 115, 196, 312}, 40] (* Harvey P. Dale, Dec 05 2018 *)
CROSSREFS
Sequence in context: A062123 A345213 A117560 * A009312 A154251 A092275
KEYWORD
nonn
STATUS
approved