A360971 Number of multisets of size n with elements from [n] whose element sum is larger than the product of all elements.

0, 0, 2, 4, 6, 8, 12, 14, 17, 20, 23, 26, 30, 33, 38, 41, 44, 47, 52, 55, 60, 63, 68, 71, 76, 78, 84, 89, 93, 97, 103, 106, 111, 115, 121, 124, 128, 131, 138, 142, 146, 151, 159, 162, 168, 171, 176, 181, 187, 190, 196, 201, 206, 210, 218, 221, 227, 232, 238

Offset: 0

Author

Alois P. Heinz, Feb 27 2023

Keywords

• nonn

Examples

			a(2) = 2: [1,1], [1,2].
a(3) = 4: [1,1,1], [1,1,2], [1,2,2], [1,1,3].
a(4) = 6: [1,1,1,1], [1,1,1,2], [1,1,2,2], [1,1,1,3], [1,1,2,3], [1,1,1,4].
a(8) = 17: [1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,2], [1,1,1,1,1,1,2,2], [1,1,1,1,1,2,2,2], [1,1,1,1,1,1,1,3], [1,1,1,1,1,1,2,3], [1,1,1,1,1,1,3,3], [1,1,1,1,1,1,1,4], [1,1,1,1,1,1,2,4], [1,1,1,1,1,1,3,4], [1,1,1,1,1,1,1,5], [1,1,1,1,1,1,2,5], [1,1,1,1,1,1,1,6], [1,1,1,1,1,1,2,6], [1,1,1,1,1,1,1,7], [1,1,1,1,1,1,2,7], [1,1,1,1,1,1,1,8].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A103586, A360538, A360563.

Programs

Maple

b:= proc(n, i, s, p) `if`(s+n*i<=p, 0, `if`(n=0 or i=1, 1, g(n, i, s, p))) end:
g:= proc(n, i, s, p) option remember; add(b(n-1, j, s+j, p*j), j=1..i) end:
a:= n-> b(n$2, 0, 1):
seq(a(n), n=0..60);

Mathematica

b[n_, i_, s_, p_] := If[s + n*i <= p, 0, If[n == 0 || i == 1, 1, g[n, i, s, p]]];
g[n_, i_, s_, p_] := g[n, i, s, p] = Sum[b[n-1, j, s+j, p*j], {j, 1, i}];
a[n_] := b[n, n, 0, 1];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 09 2023, after Alois P. Heinz *)