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 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. 5
 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, 154, 93, 48, 20, 6, 1, 0, 877, 595, 333, 169, 75, 27, 7, 1, 0, 4140, 2518, 1289, 624, 280, 110, 35, 8, 1, 0, 21147, 11591, 5394, 2442, 1071, 435, 154, 44, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Bell convolution triangle ; g.f. for column k : (x*B(x))^k with B(x) g.f. for A000110 (Bell numbers). Riordan array (1, x*B(x)), when B(x) the g.f. of A000110. Row sums are in A137551. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA Sum_{k=0..n} T(n,k) = A137551(n), n>0. EXAMPLE Triangle begins: 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, 154, 93, 48, 20, 6, 1; ... MAPLE # Uses function PMatrix from A357368. PMatrix(10, n -> combinat:-bell(n-1)); # Peter Luschny, Oct 19 2022 CROSSREFS Cf. Columns : A000007, A000110, A014322, A014323, A014325 ; Diagonals : A000012, A001477, A000096, A005586. Another version: A292870. T(2n,n) gives: A292871. Sequence in context: A059365 A106566 A099039 * A049244 A110281 A120059 Adjacent sequences: A205571 A205572 A205573 * A205575 A205576 A205577 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Jan 29 2012 STATUS approved

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Last modified December 7 23:32 EST 2022. Contains 358671 sequences. (Running on oeis4.)