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 A203154 (n-1)-st elementary symmetric function of {2, 3, 3, 4, 4, 5, 5,...,Floor[(n+4)/2]}. 3
 1, 5, 21, 102, 480, 2688, 14880, 96480, 622080, 4613760, 34110720, 285586560, 2386298880, 22289541120, 207921530880, 2145056256000, 22108972032000, 249782787072000, 2820035699712000, 34637103857664000, 425205351825408000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..502 EXAMPLE Let esf abbreviate "elementary symmetric function". Then 0th esf of {2}: 1 1st esf of {2,3}: 2+3=5; 2nd esf of {2,3,3} is 2*3+2*3+3*3=21. MAPLE SymmPolyn := proc(L::list, n::integer) local c, a, sel; a :=0 ; sel := combinat[choose](nops(L), n) ; for c in sel do a := a+mul(L[e], e=c) ; end do: a; end proc: A203154 := proc(n) [seq(floor((k+4)/2), k=1..n)] ; SymmPolyn(%, n-1); end proc: # R. J. Mathar, Sep 23 2016 # second Maple program: f:= proc(n) local L, x; if n::odd then L:= `*`(x+2, seq((x+i)\$2, i=3..2+n/2)) else L:= `*`(seq((x+i)*(x+i+1), i=2..1+n/2)) fi; coeff(L, x, 1); end proc: map(f, [\$1..50]); # Robert Israel, Nov 27 2017 MATHEMATICA f[k_] := Floor[(k + 4)/2]; t[n_] := Table[f[k], {k, 1, n}] a[n_] := SymmetricPolynomial[n - 1, t[n]] Table[a[n], {n, 1, 22}] (* A203154 *) CROSSREFS Cf. A203152, A203153, A203155. Sequence in context: A362556 A046633 A280623 * A097175 A100284 A337168 Adjacent sequences: A203151 A203152 A203153 * A203155 A203156 A203157 KEYWORD nonn AUTHOR Clark Kimberling, Dec 29 2011 STATUS approved

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Last modified June 20 10:31 EDT 2024. Contains 373516 sequences. (Running on oeis4.)