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A369289 Number of connected graphs with loops (symmetric relations) on n unlabeled vertices with at most n edges. 3
1, 2, 2, 4, 8, 17, 39, 92, 227, 573, 1482, 3883, 10343, 27786, 75392, 205933, 566166, 1564316, 4342431, 12100382, 33836606, 94903889, 266914438, 752517020, 2126292931, 6020035120, 17075411671, 48514471709, 138051863755, 393397897262, 1122523343690 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The graphs considered here can have loops but not parallel edges.
LINKS
FORMULA
a(n) = A000055(n) + A368983(n) = A000055(n) + A000081(n) + A001429(n) for n > 0.
Inverse Euler transform of A369145.
PROG
(PARI) \\ TreeGf gives gf of A000081.
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
seq(n)={my(t=TreeGf(n)); my(g(e)=subst(t + O(x*x^(n\e)), x, x^e) + O(x*x^n)); Vec(1 + (sum(d=1, n, eulerphi(d)/d*log(1/(1-g(d)))) + ((1+g(1))^2/(1-g(2))-1)/2 + 2*g(1) - 2*g(1)^2 )/2) }
CROSSREFS
Sequence in context: A108774 A063402 A175195 * A139800 A168058 A007971
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 02 2024
STATUS
approved

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Last modified July 21 16:28 EDT 2024. Contains 374475 sequences. (Running on oeis4.)