A275744 - OEIS

%I #13 Apr 13 2017 20:01:01

%S 0,1,0,2,0,0,5,1,0,0,19,2,0,0,0,85,8,1,0,0,0,509,29,2,0,0,0,0,4060,

%T 138,8,1,0,0,0,0,41301,774,33,2,0,0,0,0,0,510489,5693,153,8,1,0,0,0,0,

%U 0,7319447,53581,861,33,2,0,0,0,0,0,0,117940535,626717,6173,158,8,1

%N Triangle read by rows: Number of unlabeled cubic graphs with 2n nodes and k components.

%C Multiset transformation of A002851.

%H <a href="/index/Mu#multiplicative_completely">Index entries for triangles generated by the Multiset Transformation</a>

%F T(n,1) = A002851(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)^(-A002851(j)). - _Alois P. Heinz_, Apr 13 2017

%e The triangle starts

%e       0;

%e       1       0;

%e       2       0       0;

%e       5       1       0       0;

%e      19       2       0       0       0;

%e      85       8       1       0       0       0;

%e     509      29       2       0       0       0       0;

%e    4060     138       8       1       0       0       0       0;

%e   41301     774      33       2       0       0       0       0       0;

%e .510489    5693     153       8       1       0       0       0       0       0;

%e ...

%Y Cf. A005638 (row sums).

%K nonn,tabl

%O 1,4

%A _R. J. Mathar_, Aug 07 2016