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

0,2

Links

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

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 *)

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

Crossrefs

Sequence in context: A052808 A137157 A359810 * A340772 A370066 A076534

Adjacent sequences: A025131 A025132 A025133 * A025135 A025136 A025137

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved