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A333397
Array read by antidiagonals: T(n,k) is the number of connected k-regular multigraphs on n unlabeled nodes, loops allowed, n >= 0, k >= 0.
9
1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 3, 4, 5, 1, 0, 0, 1, 0, 3, 0, 10, 0, 1, 0, 0, 1, 1, 4, 9, 26, 28, 17, 1, 0, 0, 1, 0, 4, 0, 47, 0, 97, 0, 1, 0, 0, 1, 1, 5, 17, 91, 291, 639, 359, 71, 1, 0, 0, 1, 0, 5, 0, 149, 0, 2789, 0, 1635, 0, 1, 0, 0
OFFSET
0,18
COMMENTS
This sequence can be derived from A167625 by inverse Euler transform.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..405 (first 28 antidiagonals)
FORMULA
Column k is the inverse Euler transform of column k of A167625.
EXAMPLE
Array begins:
=========================================================
n\k | 0 1 2 3 4 5 6 7 8
----+----------------------------------------------------
0 | 1 1 1 1 1 1 1 1 1 ...
1 | 1 0 1 0 1 0 1 0 1 ...
2 | 0 1 1 2 2 3 3 4 4 ...
3 | 0 0 1 0 4 0 9 0 17 ...
4 | 0 0 1 5 10 26 47 91 149 ...
5 | 0 0 1 0 28 0 291 0 1934 ...
6 | 0 0 1 17 97 639 2789 12398 44821 ...
7 | 0 0 1 0 359 0 35646 0 1631629 ...
8 | 0 0 1 71 1635 40264 622457 8530044 89057367 ...
9 | 0 0 1 0 8296 0 14019433 0 6849428873 ...
...
CROSSREFS
Columns k=3..8 (with interspersed 0's for odd k) are: A005967, A085549, A129430, A129432, A129434, A129436.
Cf. A167625 (not necessarily connected), A322115 (not necessarily regular), A328682 (loopless), A333330.
Sequence in context: A065360 A352512 A364032 * A101676 A056560 A345415
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 18 2020
STATUS
approved