OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..24 (terms 0..21 from Alois P. Heinz)
R. Ehrenborg and A. Happ, On the powers of the descent set statistic, arXiv:1709.00778 [math.CO], 2017.
MAPLE
b:= proc(u, o, t) option remember; expand(`if`(u+o=0, 1,
add(b(u-j, o+j-1, t+1)*x^floor(2^(t-1)), j=1..u)+
add(b(u+j-1, o-j, t+1), j=1..o)))
end:
a:= n-> (p-> add(coeff(p, x, i)^n, i=0..degree(p)))(b(n, 0$2)):
seq(a(n), n=0..12);
MATHEMATICA
b[u_, o_, t_] := b[u, o, t] = Expand[If[u + o == 0, 1,
Sum[b[u - j, o + j - 1, t + 1]*x^Floor[2^(t - 1)], {j, 1, u}] +
Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}]]];
a[n_] := Function[p, Sum[Coefficient[p, x, i]^n, {i, 0, Exponent[p, x]}]][ b[n, 0, 0]];
a /@ Range[0, 12] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 09 2020
STATUS
approved