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A333158
Irregular triangle read by rows: T(n,k) is the number of k-regular graphs on n labeled nodes with loops allowed, n >= 1, 0 <= k <= n + 1.
2
1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 1, 3, 8, 8, 3, 1, 1, 0, 38, 0, 38, 0, 1, 1, 15, 208, 730, 730, 208, 15, 1, 1, 0, 1348, 0, 20670, 0, 1348, 0, 1, 1, 105, 10126, 188790, 781578, 781578, 188790, 10126, 105, 1, 1, 0, 86174, 0, 37885204, 0, 37885204, 0, 86174, 0, 1
OFFSET
1,10
COMMENTS
A loop adds 2 to the degree of its vertex.
FORMULA
T(n,k) = T(n, n+1-k).
EXAMPLE
Triangle begins:
1, 0, 1;
1, 1, 1, 1;
1, 0, 2, 0, 1;
1, 3, 8, 8, 3, 1;
1, 0, 38, 0, 38, 0, 1;
1, 15, 208, 730, 730, 208, 15, 1;
1, 0, 1348, 0, 20670, 0, 1348, 0, 1;
1, 105, 10126, 188790, 781578, 781578, 188790, 10126, 105, 1;
...
CROSSREFS
Row sums are A322635.
Columns k=0..4 are A000012, A123023, A108246, A110039 (with interspersed zeros), A228697.
Sequence in context: A276890 A276921 A339677 * A293135 A321376 A102210
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Mar 09 2020
STATUS
approved