|
|
A347940
|
|
Array T(n, k) = Sum_{j=2..n+2} (-1)^(n-j)*Stirling2(n+1, j-1)*j!*j^k/2, for n and k >= 0, read by antidiagonals.
|
|
0
|
|
|
1, 2, 2, 4, 7, 4, 8, 23, 23, 8, 16, 73, 115, 73, 16, 32, 227, 533, 533, 227, 32, 64, 697, 2359, 3451, 2359, 697, 64, 128, 2123, 10133, 20753, 20753, 10133, 2123, 128, 256, 6433, 42655, 118843, 164731, 118843, 42655, 6433, 256, 512, 19427, 177053, 657833, 1220657, 1220657, 657833, 177053, 19427, 512
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
T(m, n) is the number of saturated Cp^m*q^n-transfer systems where Cp^m*q^n is the cyclic group of order p^m*q^n, for m, n >= 0, p and q primes. See Hafeez et al. link page 1.
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = T(k,n).
T(n,k) = Sum_{j=0..min(n,k)} (j!*(j+2)!/2)*Stirling2(n+2,j+2;2)*Stirling2(k+2,j+2;2), n,k >= 0, where Stirling2(n,k;2) are the 2-Stirling numbers of the second kind A143494. - Fabián Pereyra, Jan 08 2022
|
|
EXAMPLE
|
Array begins:
1 2 4 8 16 32 ...
2 7 23 73 227 697 ...
4 23 115 533 2359 10133 ...
8 73 533 3451 20753 118843 ...
16 227 2359 20753 164731 1220657 ...
32 697 10133 118843 1220657 11467387 ...
...
|
|
PROG
|
(PARI) T(n, k) = sum(j=2, n+2, (-1)^(n-j)*stirling(n+1, j-1, 2)*j!*j^k/2);
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|