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 A275364 Triangular array read by rows: T(n,k) is the number of simple labeled graphs on n nodes whose maximal connected component has at most k nodes, n>=1, 1<=k<=n. 1
 1, 1, 2, 1, 4, 8, 1, 10, 26, 64, 1, 26, 106, 296, 1024, 1, 76, 556, 1696, 6064, 32768, 1, 232, 2752, 13392, 43968, 230896, 2097152, 1, 764, 15548, 135248, 461392, 1956816, 16886864, 268435456, 1, 2620, 99836, 1062224, 6932816, 24877904, 159248336, 2423185664, 68719476736, 1, 9496, 636056, 9621536, 130702496, 489604256, 2281210016, 24920583296, 687883494016, 35184372088832 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Alois P. Heinz, Rows n = 1..82, flattened EXAMPLE 1, 1, 2, 1, 4, 8, 1, 10, 26, 64, 1, 26, 106, 296, 1024, 1, 76, 556, 1696, 6064, 32768, 1, 232, 2752, 13392, 43968, 230896, 2097152, MAPLE with(combinat): b:= proc(n) option remember; `if`(n=0, 1, 2^(n*(n-1)/2)- add(k*binomial(n, k)*2^((n-k)*(n-k-1)/2)*b(k), k=1..n-1)/n) end: T:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(multinomial(n, n-i*j, i\$j)/j!* T(n-i*j, i-1)*b(i)^j, j=0..n/i))) end: seq(seq(T(n, k), k=1..n), n=1..12); # Alois P. Heinz, Jul 26 2016 MATHEMATICA nn = 10; f[z] := Sum[2^Binomial[n, 2] z^n/n!, {n, 0, nn}]; a = Drop[Range[0, nn]! CoefficientList[Series[Log[f[z]], {z, 0, nn}], z], 1]; Drop[Map[DeleteDuplicates, Transpose[Table[Range[0, nn]! CoefficientList[Series[Exp[Sum[a[[m]] z^m/m!, {m, 1, k}]], {z, 0, nn}], z], {k, 1, nn}]]], 1] // Grid CROSSREFS T(n,n) = A006125 for n>0. T(n,2) = A000085 for n>1. Cf. A001187. Sequence in context: A221632 A071951 A264059 * A160323 A340469 A128411 Adjacent sequences: A275361 A275362 A275363 * A275365 A275366 A275367 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Jul 24 2016 STATUS approved

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Last modified October 3 10:55 EDT 2023. Contains 365861 sequences. (Running on oeis4.)