%I #10 May 08 2024 14:56:42
%S 0,1,2,3,3,4,5,13,37,4,5,6,14,38,7,9,37,22539988369405
%N Irregular triangle read by rows, where the n-th row gives the number of steps in the hydra game (the version described in A372478) when the initial hydra is each of the A000108(n) ordered trees with n edges (ordered by lexicographic order of their corresponding Dyck words as in A063171).
%C T(4,9) = 41*2^39 - 3 = 22539988369405.
%C T(4,10) = (97*2^95+1)*2^(97*2^95-1) - 3 (1156727590779508264240712695467 digits).
%F T(n,k) = T(n-1,k)+1 if 1 <= k <= A000108(n-1).
%e Triangle begins:
%e 0;
%e 1;
%e 2, 3;
%e 3, 4, 5, 13, 37;
%e 4, 5, 6, 14, 38, 7, 9, 37, 22539988369405, ...;
%e ...
%Y Last elements on each row give A372478.
%Y Cf. A000108, A063171, A372592, A372593, A372594.
%K nonn,tabf
%O 0,3
%A _Pontus von Brömssen_, May 06 2024