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

%I A346980 #11 Apr 07 2022 03:29:26
%S A346980 1,0,0,1,8,42,215,964,4336,18490,78920,327422,1361450,5561651,
%T A346980 22748172,92064605,372730314,1498785098,6028277742,24137078144,
%U A346980 96650940881,385889337069,1540641044744,6139148609668,24462365837156,97350374411004,387401219371335
%N A346980 a(n) = A152534(n,n).
%H A346980 Alois P. Heinz, <a href="/A346980/b346980.txt">Table of n, a(n) for n = 0..100</a>
%F A346980 a(n) = A152534(n,n).
%p A346980 f:= proc(n) option remember; `if`(n<2, 1, f(n-1)*(q^n-1)/(q-1)) end:
%p A346980 b:= proc(n, i) option remember; simplify(`if`(n=0 or i=1, 1,
%p A346980       add(b(n-i*j, i-1)/f(i)^j, j=0..n/i)))
%p A346980     end:
%p A346980 a:= n-> coeff(simplify(f(n)*b(n$2)), q, n):
%p A346980 seq(a(n), n=0..26);
%t A346980 f[n_] := f[n] = If[n < 2, 1, f[n - 1]*(q^n - 1)/(q - 1)];
%t A346980 b[n_, i_] := b[n, i] = If[n == 0 || i == 1, 1,
%t A346980      Sum[b[n - i*j, i - 1]/f[i]^j, {j, 0, n/i}]];
%t A346980 a[n_] := SeriesCoefficient[f[n]*b[n, n], {q, 0, n}];
%t A346980 Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Apr 07 2022, after _Alois P. Heinz_ *)
%Y A346980 Main diagonal of A152534.
%Y A346980 Cf. A346981.
%K A346980 nonn
%O A346980 0,5
%A A346980 _Alois P. Heinz_, Aug 09 2021