login
A360563
Number of ordered multisets of size n with elements from [n] whose element sum is larger than the product of all elements.
2
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
0,3
LINKS
EXAMPLE
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].
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);
CROSSREFS
Cf. A360971.
Sequence in context: A215287 A316764 A331780 * A290061 A212031 A339032
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 27 2023
STATUS
approved