

A328863


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


1



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
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OFFSET

1,2


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.


LINKS

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


FORMULA

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


EXAMPLE

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.


CROSSREFS

Cf. A000041, A069905, A209816.
Sequence in context: A117842 A067588 A003402 * A218004 A034748 A069916
Adjacent sequences: A328860 A328861 A328862 * A328864 A328865 A328866


KEYWORD

nonn


AUTHOR

Peter Kagey, Oct 28 2019


STATUS

approved



