A275421 Triangle read by rows: T(n,k) = number of graphs with n edges and k connected components.

1, 1, 1, 3, 1, 1, 5, 4, 1, 1, 12, 8, 4, 1, 1, 30, 23, 9, 4, 1, 1, 79, 57, 26, 9, 4, 1, 1, 227, 160, 68, 27, 9, 4, 1, 1, 710, 456, 197, 71, 27, 9, 4, 1, 1, 2322, 1402, 567, 208, 72, 27, 9, 4, 1, 1, 8071, 4468, 1748, 604, 211, 72, 27, 9, 4, 1, 1, 29503, 15071, 5555, 1874

Offset

1,4

Comments

Multiset transformation of A002905.

Links

Alois P. Heinz, Rows n = 1..60, flattened

Peter Steinbach, Field Guide to Simple Graphs, Volume 4, Table 1.1a, Part 1 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Index entries for triangles generated by the Multiset Transformation

Formula

T(n,1) = A002905(n).

T(n,k) = Sum_{c_i*N_i=n,i=1..k} binomial(T(N_i,1)+c_i-1,c_i) for 1<k<=n.

G.f.: Product_{j>=1} (1-y*x^j)^(-A002905(j)). - Alois P. Heinz, Apr 13 2017

Example

      1
      1     1
      3     1     1
      5     4     1     1
     12     8     4     1     1
     30    23     9     4     1     1
     79    57    26     9     4     1     1
    227   160    68    27     9     4     1     1
    710   456   197    71    27     9     4     1     1
   2322  1402   567   208    72    27     9     4     1     1
   8071  4468  1748   604   211    72    27     9     4     1     1
  29503 15071  5555  1874   615   212    72    27     9     4     1

Mathematica

rows = 12;
A002905 = Import["https://oeis.org/A002905/b002905.txt", "Table"][[All, 2]];
gf = Product[(1 - y x^j)^-A002905[[j+1]], {j, 1, rows}];
Rest[CoefficientList[#, y]]& /@ Rest[CoefficientList[gf + O[x]^(rows+1), x]] // Flatten (* Jean-François Alcover, May 09 2019, after Alois P. Heinz *)

Crossrefs

Cf. A002905 (column 1), A000664 (row sums).

Sequence in context: A026780 A209421 A320435 * A243576 A211314 A026703

Adjacent sequences: A275418 A275419 A275420 * A275422 A275423 A275424

Keyword

nonn,tabl

Author

R. J. Mathar, Jul 27 2016

Status

approved