Search: id:A060058
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%I A060058
%S A060058 1,1,1,1,5,5,1,14,61,61,1,30,331,1385,1385,1,55,1211,12284,50521,50521,
%T A060058 1,91,3486,68060,663061,2702765,2702765,1,140,8526,281210,5162421,
%U A060058 49164554,199360981,199360981,1,204
%N A060058 Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler 
               numbers).
%C A060058 Row sums give A060059. Columns give A000012 (powers of 1), A000330 (sum 
               of squares), A060060-2 for m=0,...,4. Main diagonal gives Euler numbers 
               A000364. See triangle A060074.
%H A060058 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A060058.text">
               First 9 rows</a>.
%F A060058 a(n, m) = a(n-1, m)+((n+1-m)^2)*a(n, m-1), a(n, -1) := 0, a(0, 0)=1, 
               a(n, m)=0 if n<m.
%F A060058 a(n, m)= ay(n-m+1, m) if n >= m >= 0, with the rectangular array ay(n, 
               m) := sum((j^2)*ay(j+1, m-1), j=1..n), n >= 0, m >= 1; input: ay(n, 
               0)=1 (iterated sums of squares).
%F A060058 G.f. for m-th column: 1/(1-x) for m=0, (x^m)*sum(A060063(m, k)*x^k, k=0..m)/
               (1-x)^(3*m+1), m >= 1.
%F A060058 Recursion for g.f.s for m-th column: (1-x)*G(m, x)= x*G''(m-1, x)- G'(m-1, 
               x) + G(m-1, x)/x, m>=2; G(1, x)=x*(1+x)/(1-x)^4; the apostrophe denotes 
               differentiation w.r.t. x. G(0, x)=1/(1-x). (W. Lang, added Feb 13 
               2004.)
%e A060058 {1}; {1,1}; {1,5,5,}; {1,14,61,61}; ...
%Y A060058 Sequence in context: A154945 A011094 A075298 this_sequence A092766 A060074 
               A011501
%Y A060058 Adjacent sequences: A060055 A060056 A060057 this_sequence A060059 A060060 
               A060061
%K A060058 nonn,easy,tabl
%O A060058 0,5
%A A060058 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 16 
               2001

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