A375546 Triangle read by rows: T(n, k) = Sum_{d|n} d * A375467(d, k) for n > 0, T(0, 0) = 1.
1, 0, 1, 0, 1, 3, 0, 1, 4, 7, 0, 1, 7, 15, 19, 0, 1, 6, 26, 41, 46, 0, 1, 12, 51, 99, 123, 129, 0, 1, 8, 78, 204, 295, 330, 337, 0, 1, 15, 135, 443, 731, 883, 931, 939, 0, 1, 13, 205, 889, 1726, 2275, 2509, 2572, 2581, 0, 1, 18, 328, 1813, 4068, 5868, 6808, 7148, 7228, 7238
Offset: 0
Examples
Triangle starts: [0] 1; [1] 0, 1; [2] 0, 1, 3; [3] 0, 1, 4, 7; [4] 0, 1, 7, 15, 19; [5] 0, 1, 6, 26, 41, 46; [6] 0, 1, 12, 51, 99, 123, 129; [7] 0, 1, 8, 78, 204, 295, 330, 337; [8] 0, 1, 15, 135, 443, 731, 883, 931, 939; [9] 0, 1, 13, 205, 889, 1726, 2275, 2509, 2572, 2581;
Programs
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Maple
div := n -> numtheory:-divisors(n): T := proc(n, k) option remember; local d; if n = 0 then 1 else add(d * A375467(d, k), d = div(n)) fi end: seq(seq(T(n, k), k = 0..n), n = 0..10):
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Python
from functools import cache @cache def divisors(n): return [d for d in range(n, 0, -1) if n % d == 0] @cache def T(n, k): return sum(d * r(d, k) for d in divisors(n)) if n > 0 else 1 @cache def r(n, k): if n == 1: return int(k > 0) return sum(r(i, k) * T(n - i, k - 1) for i in range(1, n)) // (n - 1) for n in range(9): print([T(n, k) for k in range(n + 1)])