OFFSET
0,2
COMMENTS
Inverse Euler transform of A053419.
From R. J. Mathar, Jul 25 2017: (Start)
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)
LINKS
EXAMPLE
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alberto Tacchella, Jun 20 2011
EXTENSIONS
Terms a(25) and beyond from Andrew Howroyd, Oct 22 2019
STATUS
approved