cp's OEIS Frontend

A205574 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.

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