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Search: id:A155951
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| A155951 |
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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). |
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2
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| 2, 4, 17, -10, 17, 208, -88, -88, 208, 4177, -4708, 4422, -4708, 4177, 98976, -123888, 55152, 55152, -123888, 98976, 3001609, -5204582, 5360567, -4984628, 5360567, -5204582, 3001609, 105133568, -210753520, 208361232, -85444000, -85444000
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are in A151817.
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FORMULA
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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);
t(n,m)=coefficients(p(x,n))
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EXAMPLE
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{2},
{4},
{17, -10, 17},
{208, -88, -88, 208},
{4177, -4708, 4422, -4708, 4177},
{98976, -123888, 55152, 55152, -123888, 98976},
{3001609, -5204582, 5360567, -4984628, 5360567, -5204582, 3001609},
{105133568, -210753520, 208361232, -85444000, -85444000, 208361232, -210753520, 105133568},
{4300732097, -10315512136, 13267499516, -12384821752, 11302041350, -12384821752, 13267499516, -10315512136, 4300732097},
{198225072640, -539802938440, 752937755480, -641425101400, 247708437320, 247708437320, -641425101400, 752937755480, -539802938440, 198225072640},
{10243486784401, -31622720552146, 50805231998853, -55277019174408, 48150459465066, -43257991897932, 48150459465066, -55277019174408, 50805231998853, -31622720552146, 10243486784401}
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MATHEMATICA
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Clear[p, x, n, m];
p[x_, n_] = -((x - 1)^(2*n + 1)/x^n)*Sum[(k + n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]
+ Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A014221 A048872 A105510 this_sequence A118242 A006276 A103051
Adjacent sequences: A155948 A155949 A155950 this_sequence A155952 A155953 A155954
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KEYWORD
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sign,tabf
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2009
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EXTENSIONS
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Edited by N. J. A. Sloane, Jul 05 2009
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