A360563 Number of ordered multisets of size n with elements from [n] whose element sum is larger than the product of all elements.

0, 0, 3, 10, 31, 71, 171, 288, 505, 985, 1471, 2036, 3455, 5136, 8009, 11376, 14261, 17613, 24073, 34429, 60706, 76196, 92324, 108538, 144947, 167151, 201501, 309115, 452026, 543635, 649137, 928947, 1059705, 1250129, 1634194, 1838908, 2084398, 2331001, 2628518

Offset: 0

Author

Alois P. Heinz, Feb 27 2023

Keywords

• nonn

Examples

			a(2) = 3: [1,1], [1,2], [2,1].
a(3) = 10: [1,1,1], [1,1,2], [1,1,3], [1,2,1], [1,2,2], [1,3,1], [2,1,1], [2,1,2], [2,2,1], [3,1,1].
a(4) = 31: [1,1,1,1], [1,1,1,2], [1,1,1,3], [1,1,1,4], [1,1,2,1], [1,1,2,2], [1,1,2,3], [1,1,3,1], [1,1,3,2], [1,1,4,1], [1,2,1,1], [1,2,1,2], [1,2,1,3], [1,2,2,1], [1,2,3,1], [1,3,1,1], [1,3,1,2], [1,3,2,1], [1,4,1,1], [2,1,1,1], [2,1,1,2], [2,1,1,3], [2,1,2,1], [2,1,3,1], [2,2,1,1], [2,3,1,1], [3,1,1,1], [3,1,1,2], [3,1,2,1], [3,2,1,1], [4,1,1,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A360971.

Programs

Maple

b:= proc(n, i, s, p) option remember;
      `if`(s+n*i<=p, 0, `if`(n=0 or i=1, 1/n!,
       add(b(n-j, i-1, s+i*j, p*i^j)/j!, j=0..n)))
    end:
a:= n-> b(n$2, 0, 1)*n!:
seq(a(n), n=0..44);