Search: id:A134285
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%I A134285
%S A134285 1,3,1,10,3,1,35,19,3,1,126,65,19,3,1,462,331,92,19,3,1,1716,1190,421,
%T A134285 92,19,3,1,6435,5587,1805,502,92,19,3,1,24310,20613,8771,2075,502,92,19,
%U A134285 3,1,92378,92821,35726,10616,2318,502,92,19,3,1,352716,347930,160205
%N A134285 Triangle of numbers obtained from the partition array A134284.
%C A134285 This triangle is called s2(3)'.
%H A134285 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A134285.text">
               First 10 rows and more. </a>
%F A134285 a(n,m)=sum(product(s2(3;j,1)^e(n,m,q,j),j=1..n),k=1..p(n,m)) if n>=m>
               =1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions 
               of n and e(n,m,q,j) is the exponent of j in the q-th m part partition 
               of n. s2(3;n,1) = A035324(n,1) = A001700(n-1) = binomial(2*n-1,n).
%F A134285 Row sums = A001700. Triangle A134285 = A001263 * A000012 - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Nov 19 2007
%e A134285 [1];[3,1];[10,3,1];[35,19,3,1];[126,65,19,3,1];...
%e A134285 First few rows of the triangle are:
%e A134285 1;
%e A134285 2, 1;
%e A134285 5, 4, 1;
%e A134285 14, 13, 7, 1;
%e A134285 42, 41, 31, 11, 1;
%e A134285 132, 131, 116, 66, 16, 1;
%e A134285 429, 428, 407302, 127, 22, 1;
%e A134285 ...
%e A134285 a(4,2)=19 because the m=2 parts partitions (1^1,3^1) and (2^2) of n=4 
               lead to 1^1*10^1 + 3^2 =19, since A001700(n-1)=[1,3,10,...], n>=1.
%Y A134285 Row sums A134826. Alternating row sums A134827.
%Y A134285 Cf. A001700.
%Y A134285 Sequence in context: A135573 A126953 A134284 this_sequence A141811 A126954 
               A107870
%Y A134285 Adjacent sequences: A134282 A134283 A134284 this_sequence A134286 A134287 
               A134288
%K A134285 nonn,easy
%O A134285 1,2
%A A134285 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 13 2007

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