A025140 a(n) = floor(n/2)-th elementary symmetric function of C(n,0), C(n,1), ..., C(n, floor(n/2)).

1, 1, 3, 4, 34, 65, 2310, 6272, 1047424, 3973536, 3255714000, 17050908600, 69896096519040, 501898385570868, 10413963558878928048, 102159685299672000000, 10820560943026950635520000, 144743469304894583259136000, 78786195510356832343493745377280

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Maple

a:= n-> (k-> coeff(mul(binomial(n, i)*x+1, i=0..k), x, k))(iquo(n, 2)):
seq(a(n), n=0..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] + 1]];
a /@ Range[0, 18] (* 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)={ESym(binomial(n)[1..1+n\2])[n\2+1]} \\ Andrew Howroyd, Dec 19 2018

Crossrefs

Sequence in context: A269724 A296250 A032834 * A246015 A078504 A066090

Adjacent sequences: A025137 A025138 A025139 * A025141 A025142 A025143

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved