A371305 Triangle T(n,k) read by rows: number of chord diagrams with k isolated bracelets and a total of n chords.

1, 2, 1, 5, 2, 1, 17, 8, 2, 1, 79, 27, 8, 2, 1, 554, 128, 31, 8, 2, 1, 5283, 797, 143, 31, 8, 2, 1, 65346, 6939, 878, 148, 31, 8, 2, 1, 966156, 80025, 7381, 898, 148, 31, 8, 2, 1, 16411700, 1135841, 83038, 7494, 904, 148, 31, 8, 2, 1, 312700297, 18804319, 1161866, 83679, 7519, 904, 148, 31, 8, 2, 1

Offset: 1

Author

R. J. Mathar, Mar 18 2024

Keywords

• nonn
• tabl

Comments

Multiset transformation of A054499.

The row sums 1, 3, 8, 28, 117, 724, 6265, 73353, 1054650, 17639167, ... are the Euler Transform of A054499.

Examples

			T(3,2)=2: two bracelets with 3 chords in two variants (i) one bracelet with one chord and the other with 2 noncrossing chords, (ii) one bracelet with one chord and the other with 2 crossing chords.
1 ;
2 1 ;
5 2 1 ;
17 8 2 1 ;
79 27 8 2 1 ;
554 128 31 8 2 1 ;
5283 797 143 31 8 2 1 ;
65346 6939 878 148 31 8 2 1 ;
966156 80025 7381 898 148 31 8 2 1 ;
16411700 1135841 83038 7494 904 148 31 8 2 1 ;
		

Crossrefs

Cf. A054499.