Search: id:A073404
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%I A073404
%S A073404 2,12,36,96,672,1056,864,10752,40416,43968,8064,156672,1051776,2815488,
%T A073404 2396160,76032,2121984,22125312,105981696,226492416,161879040,718848,
%U A073404 27205632,404656128,2995605504
%N A073404 Coefficient triangle of polynomials (falling powers) related to convolutions 
               of A002605(n), n>=0, (generalized (2,2)-Fibonacci). Companion triangle 
               is A073403.
%C A073404 The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,
               ..
%C A073404 The k-th convolution of U0(n) := A002605(n), n>= 0, ((2,2) Fibonacci 
               numbers starting with U0(0)=1) with itself is Uk(n) := A073387(n+k,
               k) = 2*(p(k-1,n)*(n+1)*U0(n+1) + q(k-1,n)*(n+2)*U0(n))/(k!*(2^2+4*2)^k), 
               k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^(k-m),
               m=0..k) are the row polynomials of triangle b(k,m)= A073403(k,m).
%H A073404 W. Lang <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A073403_4.text">
               First 7 rows</a>.
%F A073404 Recursion for row polynomials defined in the comments: see A073405.
%e A073404 k=2: U2(n)=(2*(36+12*n)*(n+1)*U0(n+1)+2*(36+12*n)*(n+2)*U0(n))/(2!*12^2), 
               cf. A073389.
%e A073404 1; 12,36; 96,672,1056; ... (lower triangular matrix a(k,m), k >= m >= 
               0, else 0).
%Y A073404 Cf. A002605, A073387, A073403, A073405.
%Y A073404 Sequence in context: A055699 A062094 A011379 this_sequence A141208 A035597 
               A000913
%Y A073404 Adjacent sequences: A073401 A073402 A073403 this_sequence A073405 A073406 
               A073407
%K A073404 nonn,easy,tabl
%O A073404 0,1
%A A073404 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 
               2002

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