A346981 a(n) = A152474(n,n).

1, 0, 0, 1, 41, 842, 20520, 477479, 12482191, 344597977, 10325683780, 329996493091, 11307950123833, 411428962250775, 15890609817681079, 648195555340597125, 27864181100124570327, 1258096888119566215689, 59531788666265363070393, 2944807922604446013781174

Offset: 0

Author

Alois P. Heinz, Aug 09 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Main diagonal of A152474.

Cf. A346980.

Programs

Maple

f:= proc(n) option remember; `if`(n<2, 1, f(n-1)*(q^n-1)/(q-1)) end:
b:= proc(n, i) option remember; simplify(`if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)/f(i)^j/j!, j=0..n/i))))
    end:
a:= n-> coeff(simplify(n!*f(n)*b(n$2)), q, n):
seq(a(n), n=0..19);

Mathematica

f[n_] := f[n] = If[n < 2, 1, f[n - 1]*(q^n - 1)/(q - 1)];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
     Sum[b[n - i*j, i - 1]/f[i]^j/j!, {j, 0, n/i}]]];
a[n_] := SeriesCoefficient[n!*f[n]*b[n, n], {q, 0, n}];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Apr 07 2022, after Alois P. Heinz *)

Formula

a(n) = A152474(n,n).