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 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). 1
 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; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are in A151817. LINKS FORMULA 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)) EXAMPLE {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} MATHEMATICA 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[%] CROSSREFS Sequence in context: A249760 A271552 A105510 * A208132 A254206 A118242 Adjacent sequences:  A155948 A155949 A155950 * A155952 A155953 A155954 KEYWORD sign,tabf AUTHOR Roger L. Bagula, Jan 31 2009 EXTENSIONS Edited by N. J. A. Sloane, Jul 05 2009 STATUS approved

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Last modified January 20 23:47 EST 2022. Contains 350473 sequences. (Running on oeis4.)