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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 Andrew Howroyd, Table of n, a(n) for n = 0..500 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 Cf. A000055, A000081, A001429, A368983, A369145. Sequence in context: A108774 A063402 A175195 * A139800 A168058 A007971 Adjacent sequences: A369286 A369287 A369288 * A369290 A369291 A369292 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.)