Search: id:A008550
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%I A008550
%S A008550 1,1,1,1,1,1,1,2,1,1,1,5,3,1,1,1,14,11,4,1,1,1,42,45,19,5,1,1,1,132,197,
%T A008550 100,29,6,1,1,1,429,903,562,185,41,7,1,1,1,1430,4279,3304,1257,306,55,
               8,
%U A008550 1,1,1,4862,20793,20071,8925,2426,469,71,9,1,1
%N A008550 Table T(n,k), n>=0 and k>=0, read by antidiagonals: the k-th column given 
               by the k-th Narayana polynomial.
%H A008550 H. Prodinger, <a href="http://www.mat.univie.ac.at/~slc/opapers/s46proding.html">
               On a functional difference equation...</a>
%F A008550 T(n, k) = Sum_{j>0} A001263(k, j)*n^(j-1); T(n, 0)=1.
%F A008550 T(n, k) = Sum_{j, 0<=j<=k} A088617(k, j)*n^j*(1-n)^(k-j).
%e A008550 Row n=0: 1, 1, 1, 1, 1, 1, 1, 1, ... see A000012.
%e A008550 Row n=1: 1, 1, 2, 5, 14, 42, 132, 429, ... see A000108.
%e A008550 Row n=2: 1, 1, 3, 11, 45, 197, 903, 4279, ...see A001003.
%e A008550 Row n=3: 1, 1, 4, 19, 100, 562, 3304, 20071, ...see A007564.
%e A008550 Row n=4: 1, 1, 5, 29, 185, 1257, 8925, ...see A005923.
%e A008550 Row n=5: 1, 1, 6, 41, 306, 2426, 20076, ...see A078009.
%Y A008550 Other rows: A078018, A081178, A082147, A082181, A081148, A082173.
%Y A008550 Columns: A000012, A000012, A000027, A028387, A090197, A090198, A090199, 
               A090200.
%Y A008550 Main diagonal is in A099169.
%Y A008550 Sequence in context: A155586 A069739 A066060 this_sequence A064094 A090182 
               A111673
%Y A008550 Adjacent sequences: A008547 A008548 A008549 this_sequence A008551 A008552 
               A008553
%K A008550 easy,nonn,tabl
%O A008550 0,8
%A A008550 DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 23 2004

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