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.

1, 1, 2, 4, 4, 7, 7, 13, 17, 23, 26, 40, 45, 60, 64, 102, 115, 148, 169, 225, 261, 337, 375, 470, 552, 668, 780, 954, 1078, 1331, 1469, 1811, 2055, 2475, 2776, 3343, 3764, 4447, 4983, 5898, 6622, 7771, 8646, 10192, 11403, 13238, 14680, 17011, 19010, 21877

Offset: 1

Author

Vladeta Jovovic, Feb 23 2005

Keywords

• nonn

Crossrefs

Cf. A073906.

Cf. A102462, A102463.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, {1}, `if`(i<1, {},
       {seq(map(x-> x*i!^j*j!, b(n-i*j, i-1))[], j=0..n/i)})) end:
a:= n-> nops(b(n, n)):
seq(a(n), n=1..40);    # Alois P. Heinz, Apr 13 2012

Mathematica

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]];
a[n_] := Length[b[n, n]];
Array[a, 40] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)

Extensions

More terms from David Wasserman, Apr 11 2008