cp's OEIS Frontend

A264436 Triangle read by rows, inverse Bell transform of the complementary Bell numbers (A000587); T(n,k) for n>=0 and 0<=k<=n.

%I A264436 #15 Mar 26 2020 15:55:18
%S A264436 1,0,1,0,1,1,0,3,3,1,0,14,15,6,1,0,89,100,45,10,1,0,716,834,405,105,
%T A264436 15,1,0,6967,8351,4284,1225,210,21,1,0,79524,97596,52220,16009,3080,
%U A264436 378,28,1,0,1041541,1303956,721674,233268,48699,6804,630,36,1
%N A264436 Triangle read by rows, inverse Bell transform of the complementary Bell numbers (A000587); T(n,k) for n>=0 and 0<=k<=n.
%H A264436 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>
%F A264436 Row sums are A029768(n-1) for n>=1.
%F A264436 T(n,1) = A007549(n) for n>=1.
%e A264436 Triangle starts:
%e A264436 1,
%e A264436 0,     1,
%e A264436 0,     1,     1,
%e A264436 0,     3,     3,     1,
%e A264436 0,    14,    15,     6,     1,
%e A264436 0,    89,   100,    45,    10,    1,
%e A264436 0,   716,   834,   405,   105,   15,   1,
%e A264436 0,  6967,  8351,  4284,  1225,  210,  21,  1,
%e A264436 0, 79524, 97596, 52220, 16009, 3080, 378, 28, 1
%o A264436 (Sage) # uses[bell_transform from A264428, inverse_bell_transform from A264429]
%o A264436 def A264436_matrix(dim):
%o A264436     uno = [1]*dim
%o A264436     complementary_bell_numbers = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, uno))) for n in (0..dim)]
%o A264436     return inverse_bell_transform(dim, complementary_bell_numbers)
%o A264436 A264436_matrix(9)
%Y A264436 Cf. A000587, A007549, A029768, A264428, A264429.
%K A264436 nonn,tabl
%O A264436 0,8
%A A264436 _Peter Luschny_, Dec 01 2015