A098233 Consider the family of ordinary multigraphs. Sequence gives the triangle read by rows giving coefficients of polynomials arising from enumeration of those multigraphs on n edges.

1, 1, 1, 1, 1, 1, 4, 7, 3, 1, 1, 13, 46, 47, 25, 6, 1, 1, 40, 295, 587, 516, 235, 65, 10, 1, 1, 121, 1846, 6715, 9690, 7053, 3006, 800, 140, 15, 1, 1, 364, 11347, 73003, 170051, 189458, 119211, 46795, 12201, 2170, 266, 21, 1, 1, 1093, 68986, 768747

Offset

0,7

Comments

Also gives number T(n, k) of partitions of the multiset {1, 1, 2, 2, ..., n, n} into k nonempty subsets, for 2 <= k <= 2n. - Marko Riedel, Jan 22 2023

References

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

Table of n, a(n) for n=0..53.

Steve Butler, Fan Chung, Jay Cummings, and R. L. Graham, Juggling card sequences, arXiv:1504.01426 [math.CO], 2015.

L. Comtet, Birecouvrements et birevêtements d’un ensemble fini, Studia Sci. Math. Hungar 3 (1968): 137-152. [Annotated scanned copy. Warning: the table of v(n,k) has errors.]

G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Example

1,
x^2,
x^2+x^3+x^4,
x^2+4x^3+7x^4+3x^5+x^6,
x^2+13x^3+46x^4+47x^5+25x^6+6x^7+x^8,
x^2+40x^3+295x^4+587x^5+516x^6+235x^7+65x^8+10x^9+x^10,
...
Triangle starts:
1;
.  .  1;
.  .  1,  1,   1;
.  .  1,  4,   7,   3,   1;
.  .  1, 13,  46,  47,  25,   6,  1;
.  .  1, 40, 295, 587, 516, 235, 65, 10, 1;
...

Crossrefs

Cf. A360037, A360038, A360039, A020554 (row sums).

Sequence in context: A362253 A076414 A198574 * A200602 A118823 A118826

Adjacent sequences: A098230 A098231 A098232 * A098234 A098235 A098236

Keyword

nonn,tabf

Author

N. J. A. Sloane, Oct 26 2004

Status

approved