A203009 (n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(0)=2.

1, 3, 11, 50, 374, 4282, 78924, 2322060, 110101476, 8413051008, 1038251025216, 207035781419520, 66749863269991104, 34803836775900988992, 29353783726459293724224, 40050488883338399323186560, 88407698594458813846355350656

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Comments

From R. J. Mathar, Oct 01 2016 (Start):

The k-th elementary symmetric functions of the A000032(j), j=0..n-1, form a triangle T(n,k), 0<=k<=n, n>=0:

1

1 2

1 3 2

1 6 11 6

1 10 35 50 24

1 17 105 295 374 168

1 28 292 1450 3619 4282 1848

1 46 796 6706 29719 69424 78924 33264

1 75 2130 29790 224193 931275 2092220 2322060 964656

This here is the first subdiagonal. The diagonal is A135407. The 2nd column is A001610, the 3rd A242300, the 4th A213807. (End)

Crossrefs

Cf. A203010.

Programs

Mathematica

f[k_] := LucasL[k - 1]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A203009 *)