login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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

%I #7 Oct 01 2016 11:15:08

%S 1,4,19,145,1679,31146,919866,43716030,3345087696,413168662224,

%T 82432477483344,26585428576089600,13864587294260493504,

%U 11694921751248976025856,15957837208927564640940096,35227081534568618432596098240

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

%C From _R. J. Mathar_, Oct 01 2016 (Start):

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

%C 1

%C 1 1

%C 1 4 3

%C 1 8 19 12

%C 1 15 75 145 84

%C 1 26 240 970 1679 924

%C 1 44 708 5290 19139 31146 16632

%C 1 73 1984 25822 172549 586177 919866 482328

%C 1 120 5415 119070 1386183 8695980 28470185 43716030 22669416

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

%t f[k_] := LucasL[k]; t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 16}] (* A203010 *)

%Y Cf. A203009.

%K nonn

%O 1,2

%A _Clark Kimberling_, Dec 29 2011