|
|
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.
|
|
4
|
|
|
2, 3, 3, 5, 24, 5, 9, 138, 138, 9, 17, 760, 1840, 760, 17, 33, 4266, 20184, 20184, 4266, 33, 65, 24548, 210860, 376768, 210860, 24548, 65, 129, 143814, 2183652, 6233352, 6233352, 2183652, 143814, 129, 257, 851760, 22549616, 99411520, 149600448, 99411520, 22549616, 851760, 257
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
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).
|
|
EXAMPLE
|
Triangle begins as:
2;
3, 3;
5, 24, 5;
9, 138, 138, 9;
17, 760, 1840, 760, 17;
33, 4266, 20184, 20184, 4266, 33;
65, 24548, 210860, 376768, 210860, 24548, 65;
129, 143814, 2183652, 6233352, 6233352, 2183652, 143814, 129;
|
|
MATHEMATICA
|
r = 2; q = 1; 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 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|