A025134 a(n) = n-th elementary symmetric function of C(n,0), C(n,1), ..., C(n,n).

1, 2, 5, 24, 256, 6500, 407700, 64538880, 26120421376, 27252226455552, 73710997920000000, 519006451497395400000, 9544405721673726148608000, 459675814976476432499714440320, 58118199039973755223479833897882880, 19330456644008414104033256172750000000000

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Programs

Maple

a:= n-> coeff(mul(binomial(n, i)*x+1, i=0..n), x, n):
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, n}]][[n+1]];
a /@ Range[0, 15] (* Jean-François Alcover, Sep 08 2019, from PARI *)

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))[n+1]} \\ Andrew Howroyd, Dec 19 2018

Extensions

Terms a(10) and beyond from Andrew Howroyd, Dec 19 2018