cp's OEIS Frontend

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

%I A275420 #17 Jan 20 2024 15:55:44
%S A275420 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,
%T A275420 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,
%U A275420 23,14,7,4,2,1,1,18979,785,271,87,50,24,14,7,4,2,1,1,389436,19783
%N A275420 Triangle read by rows: T(n,k) = number of graphs with n nodes and k connected regular components.
%C A275420 Multiset transformation of A005177.
%C A275420 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
%H A275420 Andrew Howroyd, <a href="/A275420/b275420.txt">Table of n, a(n) for n = 1..300</a> (rows 1..24)
%H A275420 <a href="/index/Mu#&#34;multiplicative_completely">Index entries for triangles generated by the Multiset Transformation</a>
%F A275420 T(n,1) = A005177(n).
%F A275420 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.
%F A275420 G.f.: Product_{j>=1} (1-y*x^j)^(-A005177(j)). - _Alois P. Heinz_, Apr 13 2017
%e A275420       1
%e A275420       1   1
%e A275420       1   1   1
%e A275420       2   2   1   1
%e A275420       2   3   2   1   1
%e A275420       5   5   4   2   1   1
%e A275420       4   9   6   4   2   1   1
%e A275420      17  14  12   7   4   2   1   1
%e A275420      22  30  19  13   7   4   2   1   1
%e A275420     167  56  42  22  14   7   4   2   1   1
%e A275420     539 224  74  47  23  14   7   4   2   1   1
%e A275420   18979 785 271  87  50  24  14   7   4   2   1   1
%Y A275420 Cf. A005177 (1st column), A165647 (row sums).
%K A275420 nonn,tabl
%O A275420 1,7
%A A275420 _R. J. Mathar_, Jul 27 2016
%E A275420 Name clarified by _Andrew Howroyd_, May 20 2020