A203010 (n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(1)=1.

1, 4, 19, 145, 1679, 31146, 919866, 43716030, 3345087696, 413168662224, 82432477483344, 26585428576089600, 13864587294260493504, 11694921751248976025856, 15957837208927564640940096, 35227081534568618432596098240

Offset

1,2

Comments

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

The k-th elementary symmetric functions of the A000204(j), j=1..n, form a triangle T(n,k), 0<=k<=n, n>=0:

1

1 1

1 4 3

1 8 19 12

1 15 75 145 84

1 26 240 970 1679 924

1 44 708 5290 19139 31146 16632

1 73 1984 25822 172549 586177 919866 482328

1 120 5415 119070 1386183 8695980 28470185 43716030 22669416

This here is the first subdiagonal. The diagonal is A070825. The 2nd column is A027961. (End)

Links

Table of n, a(n) for n=1..16.

Mathematica

f[k_] := LucasL[k]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* A203010 *)

Crossrefs

Cf. A203009.

Sequence in context: A212717 A067577 A225904 * A362380 A249785 A341379

Adjacent sequences: A203007 A203008 A203009 * A203011 A203012 A203013

Keyword

nonn

Author

Clark Kimberling, Dec 29 2011

Status

approved