A328863 - OEIS

A328863

Number of partitions of 2n that describe the degree sequence of exactly one labeled multigraph with no loops.

%I #14 Oct 02 2023 20:21:11

%S 1,2,4,6,9,14,19,27,37,50,66,89,115,151,195,252,321,412,520,660,829,

%T 1042,1299,1623,2010,2492,3071,3783,4635,5679,6922,8434,10234,12406,

%U 14985,18085,21751,26135,31312,37471,44723,53321,63415,75336,89303,105734,124938

%N Number of partitions of 2n that describe the degree sequence of exactly one labeled multigraph with no loops.

%C Also the number of partitions of 2*n either with largest part equal to n or with three parts and largest part less than n.

%H Peter Kagey, <a href="/A328863/b328863.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000041(n) + A069905(n).

%e For n = 4, the a(4) = 6 partitions of 2*4 = 8 that describe a degree sequence of exactly one labeled multigraph are

%e 4 + 4,

%e 4 + 3 + 1,

%e 4 + 2 + 2,

%e 4 + 2 + 1 + 1,

%e 4 + 1 + 1 + 1 + 1, and

%e 3 + 3 + 2.

%Y Cf. A000041, A069905, A209816.

%K nonn

%O 1,2

%A _Peter Kagey_, Oct 28 2019