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A191970
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Number of connected graphs with n edges with loops allowed.
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15
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1, 2, 2, 6, 12, 33, 93, 287, 940, 3309, 12183, 47133, 190061, 796405, 3456405, 15501183, 71681170, 341209173, 1669411182, 8384579797, 43180474608, 227797465130, 1229915324579, 6790642656907, 38311482445514, 220712337683628, 1297542216770482, 7779452884747298
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OFFSET
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0,2
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COMMENTS
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Inverse Euler transform of A053419.
The Multiset Transform gives the number of graphs with n edges (loops allowed) and k components (0<=k<=n):
1
0 2
0 2 3
0 6 4 4
0 12 15 6 5
0 33 36 24 8 6
0 93 111 64 33 10 7
0 287 324 207 92 42 12 8
0 940 1036 633 308 120 51 14 9
0 3309 3408 2084 966 409 148 60 16 10
0 12183 11897 6959 3243 1305 510 176 69 18 11
0 47133 43137 24415 10970 4432 1644 611 204 78 20 12
0 190061 163608 88402 38763 15125 5628 1983 712 232 87 22 13
0 796405 644905 332979 140671 53732 19316 6824 2322 813 260 96 24 14
0 3456405 2639871 1299054 529179 195517 68878 23515 8020 2661 914 288 105 26 15 (End)
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LINKS
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EXAMPLE
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a(1)=2: Either one node with the edge equal to a loop, or two nodes connected by the edge. a(2)=2: Either three nodes on a chain connected by the two edges, or two nodes connected by an edge, one node with a loop. Apparently multi-loops are not allowed (?). - R. J. Mathar, Jul 25 2017
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PROG
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(PARI) \\ See A322114 for InvEulerMT, G.
seq(n)={vecsum([Vec(p+O(y^n), -n) | p<-InvEulerMT(vector(n, k, G(k, y + O(y^n))))])} \\ Andrew Howroyd, Oct 22 2019
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CROSSREFS
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Cf. A000664, A002905, A007718, A050535, A053419, A054923, A191646, A191970, A275421, A322133, A322151, A322152.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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