A154706 Triangular sequence defined by T(n, m) = Coefficients(q(x,n) + x^(n-2)*q(1/x,n))/4, where q(x, n) = d^2*p(x, n)/dx^2 and p(x, n) = 2^n*(1-x)^(n+1)*LerchPhi(x, -n, 1/2).

1, 13, 13, 118, 228, 118, 846, 3234, 3234, 846, 5279, 38932, 63258, 38932, 5279, 30339, 405927, 1082454, 1082454, 405927, 30339, 165820, 3796728, 16512132, 24852880, 16512132, 3796728, 165820, 878188, 32837380, 226681452, 509876260, 509876260, 226681452, 32837380, 878188

Offset

2,2

Links

G. C. Greubel, Rows n = 2..30 of triangle, flattened

Roger L. Bagula, Mathematica code for Fractal plot modulo two

Formula

Triangle defined by T(n, m) = Coefficients(q(x,n) + x^(n-2)*q(1/x,n))/4, where q(x, n) = d^2*p(x, n)/dx^2 and p(x, n) = 2^n*(1-x)^(n+1)* LerchPhi(x, -n, 1/2).

Example

Triangle begins as:
       1;
      13,      13;
     118,     228,      118;
     846,    3234,     3234,      846;
    5279,   38932,    63258,    38932,     5279;
   30339,  405927,  1082454,  1082454,   405927,   30339;
  165820, 3796728, 16512132, 24852880, 16512132, 3796728, 165820;

Mathematica

p[x_, n_]:= 2^n*(1-x)^(n+1)* LerchPhi[x, -n, 1/2];
q[x_, n_]:= D[p[x, n], {x, 2}];
f[n_]:= CoefficientList[FullSimplify[ExpandAll[q[x, n]]], x];
Table[(f[n] + Reverse[f[n]])/4, {n, 2, 12}]//Flatten (* modified by G. C. Greubel, May 09 2019 *)

Crossrefs

Sequence in context: A214468 A112230 A121932 * A294077 A165834 A020553

Adjacent sequences: A154703 A154704 A154705 * A154707 A154708 A154709

Keyword

nonn

Author

Roger L. Bagula, Jan 14 2009

Extensions

Edited by G. C. Greubel, May 09 2019

Status

approved