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

Author

N. J. A. Sloane, Oct 26 2004

Keywords

• nonn
• tabf

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

Examples

			The first few polynomials are:
  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;
  ...
		

References

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

Links

• 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]

Crossrefs

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