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
Keywords
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
Programs
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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);