A360563 - OEIS

%I #32 Feb 27 2023 17:05:12

%S 0,0,3,10,31,71,171,288,505,985,1471,2036,3455,5136,8009,11376,14261,

%T 17613,24073,34429,60706,76196,92324,108538,144947,167151,201501,

%U 309115,452026,543635,649137,928947,1059705,1250129,1634194,1838908,2084398,2331001,2628518

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

%H Alois P. Heinz, <a href="/A360563/b360563.txt">Table of n, a(n) for n = 0..150</a>

%e a(2) = 3: [1,1], [1,2], [2,1].

%e 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].

%e 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].

%p b:= proc(n, i, s, p) option remember;

%p       `if`(s+n*i<=p, 0, `if`(n=0 or i=1, 1/n!,

%p        add(b(n-j, i-1, s+i*j, p*i^j)/j!, j=0..n)))

%p     end:

%p a:= n-> b(n$2, 0, 1)*n!:

%p seq(a(n), n=0..44);

%Y Cf. A360971.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 27 2023