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A154695 Triangular sequence defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n), where b(n) = coefficients of p(x, n) = 2^n*(1-x)^(n+1) * LerchPhi(x, -n, 1/2), and r=2, q=1.

%I A154695 #13 Jun 03 2023 06:16:19
%S A154695 2,3,3,5,24,5,9,138,138,9,17,760,1840,760,17,33,4266,20184,20184,4266,
%T A154695 33,65,24548,210860,376768,210860,24548,65,129,143814,2183652,6233352,
%U A154695 6233352,2183652,143814,129,257,851760,22549616,99411520,149600448,99411520,22549616,851760,257
%N A154695 Triangular sequence defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n), where b(n) = coefficients of p(x, n) = 2^n*(1-x)^(n+1) * LerchPhi(x, -n, 1/2), and r=2, q=1.
%H A154695 G. C. Greubel, <a href="/A154695/b154695.txt">Rows n = 0..40 of triangle, flattened</a>
%H A154695 A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, <a href="http://dx.doi.org/10.1103/PhysRevA.34.2501">Use of combinatorial algebra for diffusion on fractals</a>, Physical Review A, volume 34, Number 3 (1986) p. 2502, Fig. 3.
%F A154695 Let r = 2 and q = 1 then b(n) = the coefficients of p(x, n) =  2^n*(1 - x)^(n + 1)* LerchPhi(x, -n, 1/2). The triangle is then defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n).
%e A154695 Triangle begins as:
%e A154695     2;
%e A154695     3,      3;
%e A154695     5,     24,       5;
%e A154695     9,    138,     138,       9;
%e A154695    17,    760,    1840,     760,      17;
%e A154695    33,   4266,   20184,   20184,    4266,      33;
%e A154695    65,  24548,  210860,  376768,  210860,   24548,     65;
%e A154695   129, 143814, 2183652, 6233352, 6233352, 2183652, 143814, 129;
%t A154695 r = 2; q = 1; p[x_, n_] = 2^n*(1-x)^(n+1)*LerchPhi[x, -n, 1/2];
%t A154695 b:= Table[CoefficientList[Series[p[x, n], {x, 0, 30}], x], {n, 0, 20}];
%t A154695 T[n_, m_]:= (r^(n-m)*q^m + r^m*q^(n-m))*b[[n+1]][[m+1]];
%t A154695 Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by _G. C. Greubel_, May 08 2019 *)
%K A154695 nonn,tabl,less
%O A154695 0,1
%A A154695 _Roger L. Bagula_ and _Gary W. Adamson_, Jan 14 2009
%E A154695 Edited by _G. C. Greubel_, May 08 2019