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A360538 Number of multisets of n nonzero digits such that sum(digits) > product(digits).

%I A360538 #43 Feb 27 2023 15:28:18
%S A360538 0,0,9,10,11,12,15,16,18,20,22,23,25,26,29,30,31,32,35,36,38,39,41,42,
%T A360538 44,44,47,50,51,52,54,55,56,57,60,60,60,61,63,64,65,67,70,71,73,73,74,
%U A360538 75,77,77,78,80,81,82,84,85,86,87,89,90,91,92,95,96,97,98,101,101
%N A360538 Number of multisets of n nonzero digits such that sum(digits) > product(digits).
%C A360538 Note that this does not represent the number of n-digit numbers that satisfy this property; that would require the computation of the permutations of each multiset.
%H A360538 Alois P. Heinz, <a href="/A360538/b360538.txt">Table of n, a(n) for n = 0..10000</a>
%e A360538 For n = 2, the a(2) = 9 solutions are [11,12,13,14,15,16,17,18,19].
%e A360538 For n = 3, the a(3) = 10 solutions are [111,112,113,114,115,116,117,118,119,122].
%p A360538 b:= proc(n, i, s, p) option remember; `if`(s+n*i<=p, 0,
%p A360538      `if`(n=0, 1, add(b(n-1, j, s+j, p*j), j=1..i)))
%p A360538     end:
%p A360538 a:= n-> b(n, 9, 0, 1):
%p A360538 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 11 2023
%Y A360538 Cf. A052382, A360971, A360972.
%K A360538 nonn,look,base
%O A360538 0,3
%A A360538 _Charles Bershatsky_, Feb 10 2023