VOOZH about

URL: https://oeis.org/A355614

⇱ A355614 - OEIS

login
A355614
Number A(n,k) of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= i^k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
3
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 5, 1, 1, 1, 8, 30, 14, 1, 1, 1, 16, 188, 340, 42, 1, 1, 1, 32, 1176, 9280, 5235, 132, 1, 1, 1, 64, 7280, 249776, 804322, 102756, 429, 1, 1, 1, 128, 44640, 6518784, 119088660, 109506040, 2464898, 1430, 1
OFFSET
0,9
LINKS
EXAMPLE
A(2,2) = 4: (1,1), (1,2), (1,3), (1,4).
A(2,3) = 8: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8).
A(3,1) = 5: (1,1,1), (1,1,2), (1,1,3), (1,2,2), (1,2,3).
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, ...
1, 5, 30, 188, 1176, 7280, ...
1, 14, 340, 9280, 249776, 6518784, ...
1, 42, 5235, 804322, 119088660, 16633660072, ...
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, add(
A(j-1, k)*(-1)^(n-j)*binomial(j^k, n-j+1), j=1..n))
end:
seq(seq(A(n, d-n), n=0..d), d=0..12);
CROSSREFS
Columns k=0-2 give: A000012, A000108, A209440.
Rows n=1-2 give: A000012, A000079.
Main diagonal gives A355613.
Sequence in context: A291118 A245184 A284414 * A140274 A095231 A303697
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 09 2022
STATUS
approved