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

1,2

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)

Links

Table of n, a(n) for n=1..17.

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 *)

Crossrefs

Cf. A203010.

Sequence in context: A256126 A321607 A024335 * A024336 A145144 A367560

Adjacent sequences: A203006 A203007 A203008 * A203010 A203011 A203012

Keyword

nonn

Author

Clark Kimberling, Dec 29 2011

Status

approved