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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Dec 19 2018
STATUS
approved