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Triangle T(n,k) read by rows in which the right border is A000041, else zero, n >= 0.
6

%I #26 Jul 25 2024 14:01:31

%S 1,0,1,0,0,2,0,0,0,3,0,0,0,0,5,0,0,0,0,0,7,0,0,0,0,0,0,11,0,0,0,0,0,0,

%T 0,15,0,0,0,0,0,0,0,0,22,0,0,0,0,0,0,0,0,0,30,0,0,0,0,0,0,0,0,0,0,42,

%U 0,0,0,0,0,0,0,0,0,0,0,56,0,0,0,0,0,0,0,0,0,0,0,0,77

%N Triangle T(n,k) read by rows in which the right border is A000041, else zero, n >= 0.

%C Eigensequence of the triangle = A058694: (1, 1, 2, 6, 30, 210,...), i.e., given A058694 preceded by a "1", triangle A174712 * the latter variant = the same sequence but shifted left.

%H Paolo Xausa, <a href="/A174712/b174712.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of the triangle, flattened).

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 0, 2;

%e 0, 0, 0, 3;

%e 0, 0, 0, 0, 5;

%e 0, 0, 0, 0, 0, 7;

%e 0, 0, 0, 0, 0, 0, 11;

%e 0, 0, 0, 0, 0, 0, 0, 15;

%e 0, 0, 0, 0, 0, 0, 0, 0, 22;

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 30;

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42;

%e ...

%t Array[PadLeft[{PartitionsP[#-1]}, #] &, 15] (* _Paolo Xausa_, Feb 21 2024 *)

%Y Cf. A000041, A058694, A174713, A174714, A174715.

%K nonn,tabl

%O 0,6

%A _Gary W. Adamson_, Mar 27 2010

%E Definition clarified by _Omar E. Pol_, Feb 21 2024