cp's OEIS Frontend

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

%I A360563 #32 Feb 27 2023 17:05:12
%S A360563 0,0,3,10,31,71,171,288,505,985,1471,2036,3455,5136,8009,11376,14261,
%T A360563 17613,24073,34429,60706,76196,92324,108538,144947,167151,201501,
%U A360563 309115,452026,543635,649137,928947,1059705,1250129,1634194,1838908,2084398,2331001,2628518
%N A360563 Number of ordered multisets of size n with elements from [n] whose element sum is larger than the product of all elements.
%H A360563 Alois P. Heinz, <a href="/A360563/b360563.txt">Table of n, a(n) for n = 0..150</a>
%e A360563 a(2) = 3: [1,1], [1,2], [2,1].
%e A360563 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 A360563 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 A360563 b:= proc(n, i, s, p) option remember;
%p A360563       `if`(s+n*i<=p, 0, `if`(n=0 or i=1, 1/n!,
%p A360563        add(b(n-j, i-1, s+i*j, p*i^j)/j!, j=0..n)))
%p A360563     end:
%p A360563 a:= n-> b(n$2, 0, 1)*n!:
%p A360563 seq(a(n), n=0..44);
%Y A360563 Cf. A360971.
%K A360563 nonn
%O A360563 0,3
%A A360563 _Alois P. Heinz_, Feb 27 2023