Search: id:A062196
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%I A062196
%S A062196 1,1,3,1,8,6,1,15,30,10,1,24,90,80,15,1,35,210,350,175,21,1,48,420,
%T A062196 1120,1050,336,28,1,63,756,2940,4410,2646,588,36,1,80,1260,6720,14700,
%U A062196 14112,5880,960,45,1,99,1980,13860
%N A062196 Coefficient triangle of certain polynomials N(2; m,x).
%C A062196 The e.g.f. of the m-th (unsigned) column sequence without leading zeros 
               of the generalized (a=2) Laguerre triangle L(2; n+m,m)= A062139(n+m,
               m), n >= 0, is N(2; m,x)/(1-x)^(3+2*m), with the row polynomials 
               N(2; m,x) := sum(a(m,k)*x^k,k=0..m).
%C A062196 Comments from Zerinvary Lajos (zlaja(AT)freemail.hu), Apr 01 2005: Formatted 
               as a square array:
%C A062196 C(2,0)*C(0,0), C(3,0)*C(1,1), C(4,0)*C(2,2), C(5,0)*C(3,3), C(6,0)*C(4,
               4), C(7,0)*C(5,5), C(8,0)*C(6,6), C(9,0)*C(7,7), C(10,0)*C(8,8)
%C A062196 C(3,1)*C(1,0), C(4,1)*C(2,1), C(5,1)*C(3,2), C(6,1)*C(4,3), C(7,1)*C(5,
               4), C(8,1)*C(6,5), C(9,1)*C(7,6), C(10,1)*C(8,7)
%C A062196 C(4,2)*C(2,0), C(5,2)*C(3,1), C(6,2)*C(4,2), C(7,2)*C(5,3), C(8,2)*C(6,
               4), C(9,2)*C(7,5), C(10,2)*C(8,6)
%C A062196 C(5,3)*C(3,0), C(6,3)*C(4,1), C(7,3)*C(5,2), C(8,3)*C(6,3), C(9,3)*C(7,
               4), C(10,3)*C(8,5)
%C A062196 C(6,4)*C(4,0), C(7,4)*C(5,1), C(8,4)*C(6,2), C(9,4)*C(7,3), C(10,4)*C(8,
               4)
%C A062196 C(7,5)*C(5,0), C(8,5)*C(6,1), C(9,5)*C(7,2), C(10,5)*C(8,3)
%C A062196 C(8,6)*C(6,0), C(9,6)*C(7,1), C(10,6)*C(8,2)
%C A062196 C(9,7)*C(7,0), C(10,7)*C(8,1)
%C A062196 C(10,8)*C(8,0)
%F A062196 a(m, k)= [x^k]N(2; m, x), with N(2; m, x)= ((1-x)^(3+2*m))*diff((x^m)/
               (m!*(1-x)^(m+3)), x$m).
%F A062196 N(2; m, x)= sum((binomial(m, j)*(2*m+2-j)!/((m+2)!*(m-j)!)*(x^(m-j)))*(1-x)^j, 
               j=0..m).
%Y A062196 A062145, A062190.
%Y A062196 Sequence in context: A021318 A068437 A016477 this_sequence A103247 A030523 
               A123965
%Y A062196 Adjacent sequences: A062193 A062194 A062195 this_sequence A062197 A062198 
               A062199
%K A062196 nonn,tabl
%O A062196 0,3
%A A062196 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 19 
               2001

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