A346980 a(n) = A152534(n,n).

1, 0, 0, 1, 8, 42, 215, 964, 4336, 18490, 78920, 327422, 1361450, 5561651, 22748172, 92064605, 372730314, 1498785098, 6028277742, 24137078144, 96650940881, 385889337069, 1540641044744, 6139148609668, 24462365837156, 97350374411004, 387401219371335

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 A152534.

Cf. A346981.

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 or i=1, 1,
      add(b(n-i*j, i-1)/f(i)^j, j=0..n/i)))
    end:
a:= n-> coeff(simplify(f(n)*b(n$2)), q, n):
seq(a(n), n=0..26);

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 || i == 1, 1,
     Sum[b[n - i*j, i - 1]/f[i]^j, {j, 0, n/i}]];
a[n_] := SeriesCoefficient[f[n]*b[n, n], {q, 0, n}];
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Apr 07 2022, after Alois P. Heinz *)

Formula

a(n) = A152534(n,n).