A025141 a(n) = (k-1)st elementary symmetric function of C(n,0), C(n,1), ..., C(n,k), where k = floor( n/2 ).

1, 1, 11, 16, 551, 1190, 178024, 564678, 410606100, 1876011225, 6915255136416, 44675417804160, 847468391006481244, 7637169791538787500, 749927054569389785088000, 9345619999880270191554560, 4766524174302701575265292220416, 81712716729371439637617531305856

Offset

2,3

Links

Andrew Howroyd, Table of n, a(n) for n = 2..50

Maple

a:= n-> (k-> coeff(mul(binomial(n, i)*x+1, i=0..k), x, k-1))(iquo(n, 2)):
seq(a(n), n=2..20);  # Alois P. Heinz, Sep 08 2019

Mathematica

ESym[u_] := Module[{v, t}, v = Table[0, {Length[u] + 1}]; v[[1]] = 1; For[i = 1, i <= Length[u], i++, t = u[[i]]; For[j = i, j >= 1, j--, v[[j + 1]] += v[[j]]*t]]; v];
a[n_] := ESym[Table[Binomial[n, k], {k, 0, Floor[n/2]}]][[Floor[n/2]]];
a /@ Range[2, 19] (* Jean-François Alcover, Sep 08 2019, from PARI *)

Prog

(PARI)
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}
a(n)={if(n>=2, ESym(binomial(n)[1..1+n\2])[n\2])} \\ Andrew Howroyd, Dec 19 2018

Crossrefs

Sequence in context: A032327 A032075 A024147 * A226678 A105709 A256546

Adjacent sequences: A025138 A025139 A025140 * A025142 A025143 A025144

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(14) and beyond from Andrew Howroyd, Dec 19 2018

Status

approved