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.

2, 5, 5, 13, 72, 13, 35, 690, 690, 35, 97, 5928, 16560, 5928, 97, 275, 49770, 302760, 302760, 49770, 275, 793, 420204, 4934124, 10172736, 4934124, 420204, 793, 2315, 3595350, 76427820, 280500840, 280500840, 76427820, 3595350, 2315

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Jan 14 2009

Keywords

• nonn
• tabl
• less

Examples

			Triangle begins as:
    2;
    5,      5;
   13,     72,      13;
   35,    690,     690,       35;
   97,   5928,   16560,     5928,      97;
  275,  49770,  302760,   302760,   49770,    275;
  793, 420204, 4934124, 10172736, 4934124, 420204, 793;
		

Links

• G. C. Greubel, Rows n = 0..40 of triangle, flattened
• A. Lakhtakia, R. Messier, V. K. Varadan, V. V. Varadan, Use of combinatorial algebra for diffusion on fractals, Physical Review A, volume 34, Number 3 (1986) p. 2502, Fig. 3.

Programs

Mathematica

r = 2; q = 3; p[x_, n_] = 2^n*(1-x)^(n+1)*LerchPhi[x, -n, 1/2];
b:= Table[CoefficientList[Series[p[x, n], {x, 0, 30}], x], {n, 0, 20}];
T[n_, m_]:= (r^(n-m)*q^m + r^m*q^(n-m))*b[[n+1]][[m+1]];
Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 08 2019 *)

Formula

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).

Extensions

Edited by G. C. Greubel, May 08 2019