A384867 Array A(T,k) read down antidiagonals: Number of typed decorated trees of cardinality T on k vertices with D=2 decorations.

2, 4, 2, 14, 8, 2, 52, 52, 12, 2, 214, 376, 114, 16, 2, 916, 2998, 1228, 200, 20, 2, 4116, 25256, 14568, 2864, 310, 24, 2, 18996, 222128, 18, 3132, 45140, 5540, 444, 28, 2

Offset

1,1

Comments

Is the array obtained by deleting each second column of A242249, transposing, and multiplying each entry by 2?

Links

Table of n, a(n) for n=1..37.

L. Foissy, Algebraic structures on typed decorated rooted trees, SIGMA 17 (2021) 086, Appendix 6.1 D=2.

Example

Array starts with rows T=1,2,3.. and columns k=1,2,3.. as
  2  4   14    52     214      916       4116      18996
  2  8   52   376    2998    25256     222128    2013680
  2 12  114  1228   14568   183132    2401410    32465640
  2 16  200  2864   45140   754640   13156232   236477200
  2 20  310  5540  108930  2272804   49446000  1109081180
  2 24  444  9512  224154  5606520  146204792  3930863232
  2 28  602 15036  413028 12043500  366122190 11475005616
  2 32  784 22368  701768 23373216  811575408 29052861280
  2 36  990 31764 1120590 41969844 1638712716 65965167108
  2 40 1220 43480 1703710 70875208 3073688160

Crossrefs

Cf. A242249 (D=1), A038055 (row 1), A136794 (row 2).

Sequence in context: A153801 A354408 A062867 * A264027 A113539 A215055

Adjacent sequences: A384864 A384865 A384866 * A384868 A384869 A384870

Keyword

nonn,tabl,more

Author

R. J. Mathar, Jun 11 2025

Status

approved