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