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A143841
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Table read by antidiagonals: T(n,k) is the number of strongly connected directed multigraphs with loops with n arcs and up to k vertices.
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3
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1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 3, 1, 0, 1, 1, 2, 4, 7, 1, 0, 1, 1, 2, 4, 11, 11, 1, 0, 1, 1, 2, 4, 12, 30, 20, 1, 0, 1, 1, 2, 4, 12, 36, 93, 29, 1, 0, 1, 1, 2, 4, 12, 37, 152, 237, 45, 1, 0, 1, 1, 2, 4, 12, 37, 161, 587, 579, 61, 1, 0
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OFFSET
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0,13
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LINKS
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FORMULA
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T(n,k) = Sum_{p=0..k} A139622(n,p).
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EXAMPLE
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Array begins:
=============================================
n\k | 0 1 2 3 4 5 6 7 8
----+----------------------------------------
0 | 1 1 1 1 1 1 1 1 1 ...
1 | 0 1 1 1 1 1 1 1 1 ...
2 | 0 1 2 2 2 2 2 2 2 ...
3 | 0 1 3 4 4 4 4 4 4 ...
4 | 0 1 7 11 12 12 12 12 12 ...
5 | 0 1 11 30 36 37 37 37 37 ...
6 | 0 1 20 93 152 161 162 162 162 ...
7 | 0 1 29 237 587 725 737 738 738 ...
8 | 0 1 45 579 2249 3610 3911 3927 3928 ...
...
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PROG
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(PARI) \\ See PARI link in A350489 for program code.
A(n)={my(T=A139622rows(n)), M=matrix(n+1, n+1, i, j, if(i==1, 1, sum(k=1, min(i-1, j-1), data[i-1][k])))); M}
{ my(M=A(8)); for(n=1, #M~, print(M[n, ])) } \\ Andrew Howroyd, Jan 14 2022
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CROSSREFS
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Partial sums of the rows of A139622.
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KEYWORD
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AUTHOR
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EXTENSIONS
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Name clarified and terms a(32) and beyond from Andrew Howroyd, Jan 14 2022
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STATUS
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approved
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