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A327372
Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with exactly k endpoints (vertices of degree 1).
5
1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 3, 1, 1, 1, 1, 11, 5, 4, 1, 2, 0, 62, 29, 18, 6, 4, 2, 1, 510, 225, 101, 32, 13, 4, 3, 0, 7459, 2674, 842, 223, 72, 19, 9, 3, 1, 197867, 50834, 10784, 2171, 504, 115, 34, 9, 4, 0, 9808968, 1653859, 228863, 32322, 5268, 944, 209, 46, 16, 4, 1
OFFSET
0,11
FORMULA
Column-wise first differences of A327371.
EXAMPLE
Triangle begins:
1
0 0
0 0 1
1 0 1 0
3 1 1 1 1
11 5 4 1 2 0
PROG
(PARI) \\ Needs G(n) defined in A327371.
T(n)={my(v=Vec(G(n)*(1 - x))); vector(#v, n, Vecrev(v[n], n))}
my(A=T(10)); for(n=1, #A, print(A[n])) \\ Andrew Howroyd, Jan 11 2024
CROSSREFS
Row sums are A002494.
Column k = 0 is A261919.
The non-covering version is A327371.
The labeled version is A327377.
Sequence in context: A200473 A361948 A180172 * A374985 A328323 A090751
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Sep 04 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Sep 11 2019
STATUS
approved