A355561 Number of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= n^(i-1).

1, 1, 2, 24, 3236, 7173370, 330736663032, 382149784071841422, 12983632019302863224103688, 14912674110246473369128526689667934, 654972005961623890774153743504185499487372010, 1228018869478731662593970252736815943512232438560622483276

Offset: 0

Author

Alois P. Heinz, Jul 06 2022

Keywords

• nonn

Examples

			a(0) = 1: ( ).
a(1) = 1: (1).
a(2) = 2: (1,1), (1,2).
a(3) = 24: (1,1,1), (1,1,2), (1,1,3), (1,1,4), (1,1,5), (1,1,6), (1,1,7), (1,1,8), (1,1,9), (1,2,2), (1,2,3), (1,2,4), (1,2,5), (1,2,6), (1,2,7), (1,2,8), (1,2,9), (1,3,3), (1,3,4), (1,3,5), (1,3,6), (1,3,7), (1,3,8), (1,3,9).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..36

Crossrefs

Main diagonal of A355576.

Cf. A076113, A090588, A107354, A355519.

Programs

Maple

b:= proc(n, k, i) option remember; `if`(n=0, 1,
      add(b(n-1, k, j), j=1..min(i, k^(n-1))))
    end:
a:= n-> b(n$2, infinity):
seq(a(n), n=0..6);
# second Maple program:
b:= proc(n, k) option remember; `if`(n=0, 1, -add(
      b(j, k)*(-1)^(n-j)*binomial(k^j, n-j), j=0..n-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..12);