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A265608 Triangle read by rows: Bell transform of A000262.

%I A265608 #15 Mar 27 2020 12:11:35
%S A265608 1,0,1,0,1,1,0,3,3,1,0,13,15,6,1,0,73,95,45,10,1,0,501,723,390,105,15,
%T A265608 1,0,4051,6405,3843,1190,210,21,1,0,37633,64615,42462,14693,3010,378,
%U A265608 28,1,0,394353,730359,519993,197442,45423,6678,630,36,1
%N A265608 Triangle read by rows: Bell transform of A000262.
%C A265608 See A264428 and the link for the definition of the Bell transform.
%H A265608 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>
%e A265608 [n\k 0      1      2      3      4     5    6   7  8]
%e A265608 [0] [1]
%e A265608 [1] [0,     1]
%e A265608 [2] [0,     1,     1]
%e A265608 [3] [0,     3,     3,     1]
%e A265608 [4] [0,    13,    15,     6,     1]
%e A265608 [5] [0,    73,    95,    45,    10,    1]
%e A265608 [6] [0,   501,   723,   390,   105,   15,   1]
%e A265608 [7] [0,  4051,  6405,  3843,  1190,  210,  21,  1]
%e A265608 [8] [0, 37633, 64615, 42462, 14693, 3010, 378, 28, 1]
%o A265608 (Sage) # uses[bell_transform from A264428]
%o A265608 def A265608_row(n):
%o A265608     fact = [factorial(k) for k in (1..n)]
%o A265608     fact2 = [sum(bell_transform(k, fact)) for k in range(n)]
%o A265608     return bell_transform(n, fact2)
%o A265608 [A265608_row(n) for n in (0..9)]
%Y A265608 Cf. A000262, A264428.
%K A265608 nonn,tabl
%O A265608 0,8
%A A265608 _Peter Luschny_, Dec 20 2015