%I A126351
%S A126351 1,1,2,1,5,4,1,9,19,8,1,14,55,65,16,1,20,125,285,211,32,1,27,245,910,
%T A126351 1351,665,64,1,35,434,2380,5901,6069,2059,128,1,44,714,5418,20181,35574,
%U A126351 26335,6305,256
%N A126351 Triangle read by rows: matrix product of the Stirling numbers of the 
               second kind with the binomial coefficients.
%C A126351 Many well-known integer sequences arise from such a matrix product of 
               combinatorial coefficients. In the present case we have as the first 
               row A000079 = the powers of two = 2^n . As the second row we have 
               A001047 = 3^n - 2^n. As the column sums we have 1,3,10,37,151,674,
               3263,17007,94828 we have A005493 = number of partitions of [n+1] 
               with a distinguished block.
%H A126351 Thomas Wieder, <a href="http://www.thomas-wieder.privat.t-online.de/">
               Home Page</a>.
%H A126351 Thomas Wieder, <a href="http://homepages.tu-darmstadt.de/~wieder">(Old) 
               Home Page</a>.
%F A126351 (In Maple notation:) Matrix product B.A 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 A126351 Matrix begins:
%e A126351 1 2 4 8 16 32 64 128 256,
%e A126351 0 1 5 19 65 211 665 2059 6305
%e A126351 0 0 1 9 55 285 1351 6069 26335
%e A126351 0 0 0 1 14 125 910 5901 35574
%e A126351 0 0 0 0 1 20 245 2380 20181
%e A126351 0 0 0 0 0 1 27 434 5418
%e A126351 0 0 0 0 0 0 1 35 714
%e A126351 0 0 0 0 0 0 0 1 44
%e A126351 0 0 0 0 0 0 0 0 1
%Y A126351 Cf. A039810, A039814, A126350, A054654, A126353.
%Y A126351 Sequence in context: A056242 A128718 A112358 this_sequence A157011 A092821 
               A110552
%Y A126351 Adjacent sequences: A126348 A126349 A126350 this_sequence A126352 A126353 
               A126354
%K A126351 nonn,tabl
%O A126351 1,3
%A A126351 Thomas Wieder (thomas.wieder(AT)t-online.de), Dec 29 2006