Search: id:A054458
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%I A054458
%S A054458 1,3,1,7,6,1,17,23,9,1,41,76,48,12,1,99,233,204,82,15,1,239,682,765,
%T A054458 428,125,18,1,577,1935,2649,1907,775,177,21,1,1393,5368,8680,7656,4010,
%U A054458 1272,238,24,1,3363,14641,27312,28548,18358,7506,1946,308,27,1,8119
%N A054458 Convolution triangle based on A001333(n), n >= 1.
%C A054458 In the language of the Shapiro et al. reference (given in A053121) such 
               a lower triangular (ordinary) convolution array, considered as a 
               matrix, belongs to the Bell-subgroup of the Riordan-group.
%C A054458 The G.f. for the row polynomials p(n,x) (increasing powers of x) is LPell(z)/
               (1-x*z*LPell(z)) with LPell(z) given in 'Formula'.
%C A054458 Column sequences are A001333(n+1), A054459(n), A054460(n) for m=0..2.
%F A054458 a(n, m) := ((n-m+1)*a(n, m-1) + (2n-m)*a(n-1, m-1) + (n-1)*a(n-2, m-1))/
               (4*m), n >= m >= 1; a(n, 0)= A001333(n+1); a(n, m) := 0 if n<m.
%F A054458 G.f. for column m: LPell(x)*(x*LPell(x))^m, m >= 0, with LPell(x)= (1+x)/
               (1-2*x-x^2) = g.f. for A001333(n+1).
%e A054458 {1}; {3,1}; {7,6,1}; {17,23,9,1};...
%e A054458 Fourth row polynomial (n=3): p(3,x)= 17+23*x+9*x^2+x^3
%Y A054458 Cf. A002203(n+1)/2. Row sums: A055099(n).
%Y A054458 Sequence in context: A101624 A110441 A111806 this_sequence A110168 A046913 
               A118228
%Y A054458 Adjacent sequences: A054455 A054456 A054457 this_sequence A054459 A054460 
               A054461
%K A054458 easy,nonn,tabl
%O A054458 0,2
%A A054458 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 26 
               2000

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