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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

%I #8 Jun 03 2023 06:29:35

%S 1,13,13,118,228,118,846,3234,3234,846,5279,38932,63258,38932,5279,

%T 30339,405927,1082454,1082454,405927,30339,165820,3796728,16512132,

%U 24852880,16512132,3796728,165820,878188,32837380,226681452,509876260,509876260,226681452,32837380,878188

%N 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).

%H G. C. Greubel, <a href="/A154706/b154706.txt">Rows n = 2..30 of triangle, flattened</a>

%H Roger L. Bagula, <a href="/A154706/a154706.txt">Mathematica code for Fractal plot modulo two</a>

%F 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).

%e Triangle begins as:

%e 1;

%e 13, 13;

%e 118, 228, 118;

%e 846, 3234, 3234, 846;

%e 5279, 38932, 63258, 38932, 5279;

%e 30339, 405927, 1082454, 1082454, 405927, 30339;

%e 165820, 3796728, 16512132, 24852880, 16512132, 3796728, 165820;

%t p[x_, n_]:= 2^n*(1-x)^(n+1)* LerchPhi[x, -n, 1/2];

%t q[x_, n_]:= D[p[x, n], {x, 2}];

%t f[n_]:= CoefficientList[FullSimplify[ExpandAll[q[x, n]]], x];

%t Table[(f[n] + Reverse[f[n]])/4, {n, 2, 12}]//Flatten (* modified by _G. C. Greubel_, May 09 2019 *)

%K nonn

%O 2,2

%A _Roger L. Bagula_, Jan 14 2009

%E Edited by _G. C. Greubel_, May 09 2019