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

%I A346981 #11 Apr 07 2022 03:28:22
%S A346981 1,0,0,1,41,842,20520,477479,12482191,344597977,10325683780,
%T A346981 329996493091,11307950123833,411428962250775,15890609817681079,
%U A346981 648195555340597125,27864181100124570327,1258096888119566215689,59531788666265363070393,2944807922604446013781174
%N A346981 a(n) = A152474(n,n).
%H A346981 Alois P. Heinz, <a href="/A346981/b346981.txt">Table of n, a(n) for n = 0..100</a>
%F A346981 a(n) = A152474(n,n).
%p A346981 f:= proc(n) option remember; `if`(n<2, 1, f(n-1)*(q^n-1)/(q-1)) end:
%p A346981 b:= proc(n, i) option remember; simplify(`if`(n=0, 1, `if`(i<1, 0,
%p A346981       add(b(n-i*j, i-1)/f(i)^j/j!, j=0..n/i))))
%p A346981     end:
%p A346981 a:= n-> coeff(simplify(n!*f(n)*b(n$2)), q, n):
%p A346981 seq(a(n), n=0..19);
%t A346981 f[n_] := f[n] = If[n < 2, 1, f[n - 1]*(q^n - 1)/(q - 1)];
%t A346981 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
%t A346981      Sum[b[n - i*j, i - 1]/f[i]^j/j!, {j, 0, n/i}]]];
%t A346981 a[n_] := SeriesCoefficient[n!*f[n]*b[n, n], {q, 0, n}];
%t A346981 Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Apr 07 2022, after _Alois P. Heinz_ *)
%Y A346981 Main diagonal of A152474.
%Y A346981 Cf. A346980.
%K A346981 nonn
%O A346981 0,5
%A A346981 _Alois P. Heinz_, Aug 09 2021