A275420 Triangle read by rows: T(n,k) = number of graphs with n nodes and k connected regular components.

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 5, 5, 4, 2, 1, 1, 4, 9, 6, 4, 2, 1, 1, 17, 14, 12, 7, 4, 2, 1, 1, 22, 30, 19, 13, 7, 4, 2, 1, 1, 167, 56, 42, 22, 14, 7, 4, 2, 1, 1, 539, 224, 74, 47, 23, 14, 7, 4, 2, 1, 1, 18979, 785, 271, 87, 50, 24, 14, 7, 4, 2, 1, 1, 389436, 19783

Offset: 1

Author

R. J. Mathar, Jul 27 2016

Keywords

• nonn
• tabl

Comments

Multiset transformation of A005177.

The resulting graph has each component regular but may not be regular itself since different components can have different degrees. - Andrew Howroyd, May 20 2020

Examples

			      1
      1   1
      1   1   1
      2   2   1   1
      2   3   2   1   1
      5   5   4   2   1   1
      4   9   6   4   2   1   1
     17  14  12   7   4   2   1   1
     22  30  19  13   7   4   2   1   1
    167  56  42  22  14   7   4   2   1   1
    539 224  74  47  23  14   7   4   2   1   1
  18979 785 271  87  50  24  14   7   4   2   1   1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..300 (rows 1..24)
• Index entries for triangles generated by the Multiset Transformation

Crossrefs

Cf. A005177 (1st column), A165647 (row sums).

Formula

T(n,1) = A005177(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

G.f.: Product_{j>=1} (1-y*x^j)^(-A005177(j)). - Alois P. Heinz, Apr 13 2017

Extensions

Name clarified by Andrew Howroyd, May 20 2020

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