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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 (list; table; graph; refs; listen; history; text; internal format)
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: A031267 A247763 A065360 * A101676 A056560 A096608

Adjacent sequences:  A333394 A333395 A333396 * A333398 A333399 A333400

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Mar 18 2020

STATUS

approved

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Last modified July 8 03:38 EDT 2020. Contains 335504 sequences. (Running on oeis4.)