A328863 Number of partitions of 2n that describe the degree sequence of exactly one labeled multigraph with no loops.

1, 2, 4, 6, 9, 14, 19, 27, 37, 50, 66, 89, 115, 151, 195, 252, 321, 412, 520, 660, 829, 1042, 1299, 1623, 2010, 2492, 3071, 3783, 4635, 5679, 6922, 8434, 10234, 12406, 14985, 18085, 21751, 26135, 31312, 37471, 44723, 53321, 63415, 75336, 89303, 105734, 124938

Offset: 1

Author

Peter Kagey, Oct 28 2019

Keywords

• nonn

Comments

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.

Examples

			For n = 4, the a(4) = 6 partitions of 2*4 = 8 that describe a degree sequence of exactly one labeled multigraph are
  4 + 4,
  4 + 3 + 1,
  4 + 2 + 2,
  4 + 2 + 1 + 1,
  4 + 1 + 1 + 1 + 1, and
  3 + 3 + 2.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000041, A069905, A209816.

Formula

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