Search: id:A155951
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%I A155951
%S A155951 2,4,17,10,17,208,88,88,208,4177,4708,4422,4708,4177,98976,123888,
%T A155951 55152,55152,123888,98976,3001609,5204582,5360567,4984628,5360567,
%U A155951 5204582,3001609,105133568,210753520,208361232,85444000,85444000
%V A155951 2,4,17,-10,17,208,-88,-88,208,4177,-4708,4422,-4708,4177,98976,-123888,
%W A155951 55152,55152,-123888,98976,3001609,-5204582,5360567,-4984628,5360567,
%X A155951 -5204582,3001609,105133568,-210753520,208361232,-85444000,-85444000
%N A155951 Triangle read by rows. Let q(x,n) = -((x - 1)^(2*n + 1)/x^n)*Sum[(k + 
               n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/
               x,n); then row n gives coefficients of p(x,n).
%C A155951 Row sums are in A151817.
%F A155951 q(x,n)=-((x - 1)^(2*n + 1)/x^n)*Sum[(k + n)^n*Binomial[k, n]*x^k, {k, 
               0, Infinity}];
%F A155951 p(x,n)=q(x,n)+x^n*q(1/x,n);
%F A155951 t(n,m)=coefficients(p(x,n))
%e A155951 {2},
%e A155951 {4},
%e A155951 {17, -10, 17},
%e A155951 {208, -88, -88, 208},
%e A155951 {4177, -4708, 4422, -4708, 4177},
%e A155951 {98976, -123888, 55152, 55152, -123888, 98976},
%e A155951 {3001609, -5204582, 5360567, -4984628, 5360567, -5204582, 3001609},
%e A155951 {105133568, -210753520, 208361232, -85444000, -85444000, 208361232, -210753520, 
               105133568},
%e A155951 {4300732097, -10315512136, 13267499516, -12384821752, 11302041350, -12384821752, 
               13267499516, -10315512136, 4300732097},
%e A155951 {198225072640, -539802938440, 752937755480, -641425101400, 247708437320, 
               247708437320, -641425101400, 752937755480, -539802938440, 198225072640},
%e A155951 {10243486784401, -31622720552146, 50805231998853, -55277019174408, 48150459465066, 
               -43257991897932, 48150459465066, -55277019174408, 50805231998853, 
               -31622720552146, 10243486784401}
%t A155951 Clear[p, x, n, m];
%t A155951 p[x_, n_] = -((x - 1)^(2*n + 1)/x^n)*Sum[(k + n)^n*Binomial[k, n]*x^k, 
               {k, 0, Infinity}];
%t A155951 Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
%t A155951 Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]
%t A155951 + Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 
               0, 10}];
%t A155951 Flatten[%]
%Y A155951 Sequence in context: A014221 A048872 A105510 this_sequence A118242 A006276 
               A103051
%Y A155951 Adjacent sequences: A155948 A155949 A155950 this_sequence A155952 A155953 
               A155954
%K A155951 sign,tabf
%O A155951 0,1
%A A155951 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2009
%E A155951 Edited by N. J. A. Sloane, Jul 05 2009

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