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

%I A384867 #11 Jun 11 2025 09:57:08
%S A384867 2,4,2,14,8,2,52,52,12,2,214,376,114,16,2,916,2998,1228,200,20,2,4116,
%T A384867 25256,14568,2864,310,24,2,18996,222128,18,3132,45140,5540,444,28,2
%N A384867 Array A(T,k) read down antidiagonals: Number of typed decorated trees of cardinality T on k vertices with D=2 decorations.
%C A384867 Is the array obtained by deleting each second column of A242249, transposing, and multiplying each entry by 2?
%H A384867 L. Foissy, <a href="https://doi.org/10.3852/SIGMA.2021.086">Algebraic structures on typed decorated rooted trees</a>, SIGMA 17 (2021) 086, Appendix 6.1 D=2.
%e A384867 Array starts with rows T=1,2,3.. and columns k=1,2,3.. as
%e A384867   2  4   14    52     214      916       4116      18996
%e A384867   2  8   52   376    2998    25256     222128    2013680
%e A384867   2 12  114  1228   14568   183132    2401410    32465640
%e A384867   2 16  200  2864   45140   754640   13156232   236477200
%e A384867   2 20  310  5540  108930  2272804   49446000  1109081180
%e A384867   2 24  444  9512  224154  5606520  146204792  3930863232
%e A384867   2 28  602 15036  413028 12043500  366122190 11475005616
%e A384867   2 32  784 22368  701768 23373216  811575408 29052861280
%e A384867   2 36  990 31764 1120590 41969844 1638712716 65965167108
%e A384867   2 40 1220 43480 1703710 70875208 3073688160
%Y A384867 Cf. A242249 (D=1), A038055 (row 1), A136794 (row 2).
%K A384867 nonn,tabl,more
%O A384867 1,1
%A A384867 _R. J. Mathar_, Jun 11 2025