OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1275 (rows n = 1..50, flattened)
Mohammad K. Azarian, Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141.
EXAMPLE
For T(2,2), the number of relations is 2^4 and the number of onto functions is 2, so 2^4 - 2 = 14.
Triangle T(n,k) begins:
1
3 14
7 58 506
15 242 4060 65512
31 994 32618 1048336 33554312
MATHEMATICA
TableForm[Table[2^(n*k) - Sum[Binomial[k, k - i] (k - i)^n*(-1)^i, {i, 0, k}], {n, 5}, {k, n}]]
PROG
(PARI) T(n, k) = 2^(n*k) - k!*stirling(n, k, 2); \\ Michel Marcus, Jun 26 2021
CROSSREFS
KEYWORD
AUTHOR
Mohammad K. Azarian, Jun 07 2021
STATUS
approved