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A155950 A triangle of polynomial coefficients: q(x,n)=(1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n). 0

%I

%S 1,1,2,2,8,8,26,22,22,26,272,-64,352,-64,272,2882,-486,1444,1444,-486,

%T 2882,50752,-93056,230336,-283904,230336,-93056,50752,745418,-1182562,

%U 2112618,-1030354,-1030354,2112618,-1182562,745418,18456832,-66045952

%N A triangle of polynomial coefficients: q(x,n)=(1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n).

%C Row sums are:

%C {2, 4, 16, 96, 768, 7680, 92160, 1290240, 20643840, 371589120, 7431782400,...}.

%F q(x,n)=(1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}];

%F p(x,n)=q(x,n)+x^n*q(1/x,n);

%F t(n,m)=coefficients(p(x,n))

%e {1, 1},

%e {2, 2},

%e {8, 8},

%e {26, 22, 22, 26},

%e {272, -64, 352, -64, 272},

%e {2882, -486, 1444, 1444, -486, 2882}, {50752, -93056, 230336, -283904, 230336, -93056, 50752},

%e {745418, -1182562, 2112618, -1030354, -1030354, 2112618, -1182562, 745418},

%e {18456832, -66045952, 193838080, -342063104, 412272128, -342063104, 193838080, -66045952, 18456832},

%e {347066882, -1114674254, 2662543720, -3229707896, 1520566108, 1520566108, -3229707896, 2662543720, -1114674254, 347066882},

%e {11073741824, -59833329664, 216555369472, -500687839232, 812895791104, -952575684608, 812895791104, -500687839232, 216555369472, -59833329664, 11073741824}

%t Clear[p, x, n, m];

%t p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + n)^n*x^k, {k, 0, Infinity}];

%t Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]

%t + Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}];

%t Flatten[%]

%K sign,tabl,uned

%O 0,3

%A _Roger L. Bagula_, Jan 31 2009

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Last modified May 24 21:58 EDT 2022. Contains 354043 sequences. (Running on oeis4.)