Search: id:A126350
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%I A126350
%S A126350 1,1,2,1,5,5,1,9,22,15,1,14,61,99,52,1,20,135,385,471,203,1,27,260,1140,
%T A126350 2416,2386,877,1,35,455,2835,9156,15470,12867,4140,1,44,742,6230,28441,
%U A126350 72590,102215,73681,21147
%N A126350 Triangle read by rows: matrix product of the binomial coefficients with 
               the Stirling numbers of the second kind.
%C A126350 Many well-known integer sequences arise from such a matrix product of 
               combinatorial coefficients. In the present case we have as the first 
               row (not surprisingly) A000110 = Bell or exponential numbers: ways 
               of placing n labeled balls into n indistinguishable boxes . As second 
               row we have A033452 = "STIRLING" transform of squares A000290. As 
               the column sums we have 1, 3, 11, 47, 227, 1215, 7107, 44959, 305091 
               which is A035009 = STIRLING transform of [1,1,2,4,8,16,32, ...].
%H A126350 Thomas Wieder, <a href="http://www.thomas-wieder.privat.t-online.de/">
               Home Page</a>.
%H A126350 Thomas Wieder, <a href="http://homepages.tu-darmstadt.de/~wieder">(Old) 
               Home Page</a>.
%F A126350 (In Maple notation:) Matrix product A.B of matrix A[i,j]:=binomial(j-1,
               i-1) with i = 1 to p+1, j = 1 to p+1, p=8 and of matrix B[i,j]:=stirling2(j,
               i) with i from 1 to d, j from 1 to d, d=9.
%e A126350 Matrix begins:
%e A126350 1 2 5 15 52 203 877 4140 21147
%e A126350 0 1 5 22 99 471 2386 12867 73681
%e A126350 0 0 1 9 61 385 2416 15470 102215
%e A126350 0 0 0 1 14 135 1140 9156 72590
%e A126350 0 0 0 0 1 20 260 2835 28441
%e A126350 0 0 0 0 0 1 27 455 6230
%e A126350 0 0 0 0 0 0 1 35 742
%e A126350 0 0 0 0 0 0 0 1 44
%e A126350 0 0 0 0 0 0 0 0 1
%Y A126350 Cf. A039810, A039814, A126351, A054654, A126353.
%Y A126350 Sequence in context: A111785 A021468 A033282 this_sequence A079502 A126124 
               A060920
%Y A126350 Adjacent sequences: A126347 A126348 A126349 this_sequence A126351 A126352 
               A126353
%K A126350 nonn,tabl
%O A126350 1,3
%A A126350 Thomas Wieder (thomas.wieder(AT)t-online.de), Dec 29 2006

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