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%I #19 Oct 19 2022 11:05:22
%S 1,0,1,0,1,1,0,2,2,1,0,5,5,3,1,0,15,14,9,4,1,0,52,44,28,14,5,1,0,203,
%T 154,93,48,20,6,1,0,877,595,333,169,75,27,7,1,0,4140,2518,1289,624,
%U 280,110,35,8,1,0,21147,11591,5394,2442,1071,435,154,44,9,1
%N Triangle T(n,k), 0<=k<=n, given by (0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C Bell convolution triangle ; g.f. for column k : (x*B(x))^k with B(x) g.f. for A000110 (Bell numbers).
%C Riordan array (1, x*B(x)), when B(x) the g.f. of A000110.
%C Row sums are in A137551.
%H Alois P. Heinz, <a href="/A205574/b205574.txt">Rows n = 0..140, flattened</a>
%F Sum_{k=0..n} T(n,k) = A137551(n), n>0.
%e Triangle begins:
%e 1;
%e 0, 1;
%e 0, 1, 1;
%e 0, 2, 2, 1;
%e 0, 5, 5, 3, 1;
%e 0, 15, 14, 9, 4, 1;
%e 0, 52, 44, 28, 14, 5, 1;
%e 0, 203, 154, 93, 48, 20, 6, 1;
%e ...
%p # Uses function PMatrix from A357368.
%p PMatrix(10, n -> combinat:-bell(n-1)); # _Peter Luschny_, Oct 19 2022
%Y Cf. Columns : A000007, A000110, A014322, A014323, A014325 ; Diagonals : A000012, A001477, A000096, A005586.
%Y Another version: A292870.
%Y T(2n,n) gives: A292871.
%K easy,nonn,tabl
%O 0,8
%A _Philippe Deléham_, Jan 29 2012
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