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%I #24 Dec 19 2018 15:06:06
%S 1,4,22,238,5825,345600,51583084,19765932032,19661794008192,
%T 51082239411000000,347836712523276735000,6221718604078720792473600,
%U 292819054882445795002015111824,36313083181879002042916296055971840,11881691691176915544450299522846484375000
%N (n-1)st elementary symmetric function of binomial(n,0), binomial(n,1), ..., binomial(n,n).
%C From _R. J. Mathar_, Oct 01 2016: (Start)
%C The k-th elementary symmetric functions of the terms binomial(n,j), j=0..n, form a triangle T(n,k), 0 <= k <= n, n >= 0:
%C 1
%C 1 2
%C 1 4 5
%C 1 8 22 24
%C 1 16 93 238 256
%C 1 32 386 2180 5825 6500
%C 1 64 1586 19184 117561 345600 407700
%C 1 128 6476 164864 2229206 15585920 51583084 64538880
%C ...
%C This here is the first subdiagonal. The diagonal is A025134. The 2nd column is A000079, the 2nd A000346, the 3rd A025131, the 4th A025133. (End)
%H Vincenzo Librandi, <a href="/A025135/b025135.txt">Table of n, a(n) for n = 1..70</a>
%t a[n_] := SymmetricPolynomial[n-1, Table[Binomial[n, k], {k, 0, n}]]; a /@ Range[18] (* _Jean-François Alcover_, Jul 12 2011 *)
%o (PARI)
%o ESym(u)={my(v=vector(#u+1)); v[1]=1; for(i=1, #u, my(t=u[i]); forstep(j=i, 1,-1, v[j+1]+=v[j]*t)); v}
%o a(n)={ESym(binomial(n))[n]} \\ _Andrew Howroyd_, Dec 19 2018
%K nonn
%O 1,2
%A _Clark Kimberling_
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