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A154696 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=3.

%I A154696 #13 Jun 03 2023 06:21:05
%S A154696 2,5,5,13,72,13,35,690,690,35,97,5928,16560,5928,97,275,49770,302760,
%T A154696 302760,49770,275,793,420204,4934124,10172736,4934124,420204,793,2315,
%U A154696 3595350,76427820,280500840,280500840,76427820,3595350,2315
%N A154696 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=3.
%H A154696 G. C. Greubel, <a href="/A154696/b154696.txt">Rows n = 0..40 of triangle, flattened</a>
%H A154696 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 A154696 Let r = 2 and q = 3 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 A154696 Triangle begins as:
%e A154696     2;
%e A154696     5,      5;
%e A154696    13,     72,      13;
%e A154696    35,    690,     690,       35;
%e A154696    97,   5928,   16560,     5928,      97;
%e A154696   275,  49770,  302760,   302760,   49770,    275;
%e A154696   793, 420204, 4934124, 10172736, 4934124, 420204, 793;
%t A154696 r = 2; q = 3; p[x_, n_] = 2^n*(1-x)^(n+1)*LerchPhi[x, -n, 1/2];
%t A154696 b:= Table[CoefficientList[Series[p[x, n], {x, 0, 30}], x], {n, 0, 20}];
%t A154696 T[n_, m_]:= (r^(n-m)*q^m + r^m*q^(n-m))*b[[n+1]][[m+1]];
%t A154696 Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by _G. C. Greubel_, May 08 2019 *)
%K A154696 nonn,tabl,less
%O A154696 0,1
%A A154696 _Roger L. Bagula_ and _Gary W. Adamson_, Jan 14 2009
%E A154696 Edited by _G. C. Greubel_, May 08 2019