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A102465 a(n) = number of distinct values of Product_{i=1..r} x_i!*i!^x_i, where (x_1, ..., x_r) is an r-tuple of nonnegative integers with Sum_{i=1..r} i*x_i = n.

%I A102465 #15 Nov 09 2020 09:13:26
%S A102465 1,1,2,4,4,7,7,13,17,23,26,40,45,60,64,102,115,148,169,225,261,337,
%T A102465 375,470,552,668,780,954,1078,1331,1469,1811,2055,2475,2776,3343,3764,
%U A102465 4447,4983,5898,6622,7771,8646,10192,11403,13238,14680,17011,19010,21877
%N A102465 a(n) = number of distinct values of Product_{i=1..r} x_i!*i!^x_i, where (x_1, ..., x_r) is an r-tuple of nonnegative integers with Sum_{i=1..r} i*x_i = n.
%p A102465 b:= proc(n, i) option remember; `if`(n=0, {1}, `if`(i<1, {},
%p A102465        {seq(map(x-> x*i!^j*j!, b(n-i*j, i-1))[], j=0..n/i)})) end:
%p A102465 a:= n-> nops(b(n, n)):
%p A102465 seq(a(n), n=1..40);    # _Alois P. Heinz_, Apr 13 2012
%t A102465 b[n_, i_] := b[n, i] = If[n == 0, {1}, If[i < 1, {}, Table[# i!^j j!& /@ b[n - i j, i - 1], {j, 0, n/i}] // Flatten // Union]];
%t A102465 a[n_] := Length[b[n, n]];
%t A102465 Array[a, 40] (* _Jean-François Alcover_, Nov 09 2020, after _Alois P. Heinz_ *)
%Y A102465 Cf. A073906.
%Y A102465 Cf. A102462, A102463.
%K A102465 nonn
%O A102465 1,3
%A A102465 _Vladeta Jovovic_, Feb 23 2005
%E A102465 More terms from _David Wasserman_, Apr 11 2008