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

1,2

Comments

Multiset transformation of A054499.

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

Links

Table of n, a(n) for n=1..66.

Example

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.

Sequence in context: A047848 A275431 A281348 * A308698 A308569 A350073

Adjacent sequences: A371302 A371303 A371304 * A371306 A371307 A371308

Keyword

nonn,tabl

Author

R. J. Mathar, Mar 18 2024

Status

approved