A360972 Number of n-digit zeroless numbers whose digit sum is larger than the product of all digits.

0, 0, 17, 28, 51, 91, 189, 302, 513, 985, 1461, 1904, 3155, 4616, 7211, 10236, 12709, 15573, 21463, 31161, 56306, 70904, 85570, 100626, 135203, 155951, 188059, 293887, 434106, 522755, 612837, 888740, 1013337, 1182809, 1559292, 1755888, 1971286, 2208087, 2491034

Offset: 0

Author

Alois P. Heinz, Feb 27 2023

Keywords

• nonn
• base

Examples

			a(2) = 17: 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91.
a(3) = 28: 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 131, 141, 151, 161, 171, 181, 191, 211, 212, 221, 311, 411, 511, 611, 711, 811, 911.
a(4) = 51: 1111, 1112, 1113, 1114, ..., 6111, 7111, 8111, 9111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007953, A007954, A052382, A055642, A360538.

Programs

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, 9, 0, 1)*n!:
seq(a(n), n=0..40);

Formula

a(n) = |{ k in { A052382 } : A055642(k) = n and A007953(k) > A007954(k) }|.