A346981 - OEIS

%I #11 Apr 07 2022 03:28:22

%S 1,0,0,1,41,842,20520,477479,12482191,344597977,10325683780,

%T 329996493091,11307950123833,411428962250775,15890609817681079,

%U 648195555340597125,27864181100124570327,1258096888119566215689,59531788666265363070393,2944807922604446013781174

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

%H Alois P. Heinz, <a href="/A346981/b346981.txt">Table of n, a(n) for n = 0..100</a>

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

%p f:= proc(n) option remember; `if`(n<2, 1, f(n-1)*(q^n-1)/(q-1)) end:

%p b:= proc(n, i) option remember; simplify(`if`(n=0, 1, `if`(i<1, 0,

%p       add(b(n-i*j, i-1)/f(i)^j/j!, j=0..n/i))))

%p     end:

%p a:= n-> coeff(simplify(n!*f(n)*b(n$2)), q, n):

%p seq(a(n), n=0..19);

%t f[n_] := f[n] = If[n < 2, 1, f[n - 1]*(q^n - 1)/(q - 1)];

%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,

%t      Sum[b[n - i*j, i - 1]/f[i]^j/j!, {j, 0, n/i}]]];

%t a[n_] := SeriesCoefficient[n!*f[n]*b[n, n], {q, 0, n}];

%t Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Apr 07 2022, after _Alois P. Heinz_ *)

%Y Main diagonal of A152474.

%Y Cf. A346980.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Aug 09 2021