|
|
A134082
|
|
Triangle read by rows, (n-1) zeros followed by (2n, 1).
|
|
9
|
|
|
1, 2, 1, 0, 4, 1, 0, 0, 6, 1, 0, 0, 0, 8, 1, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 12, 1, 0, 0, 0, 0, 0, 0, 14, 1, 0, 0, 0, 0, 0, 0, 0, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 18, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
A112295 replaces subdiagonal with (-1,-3,-5, ...).
|
|
LINKS
|
|
|
FORMULA
|
Triangle read by rows, (n-1) zeros followed by (2n, 1). As an infinite lower triangular matrix, (1,1,1,...) in the main diagonal and (2,4,6,8,...) in the subdiagonal.
From formalism in A132382, e.g.f. = I_o[2*(u*x)^(1/2)] (1+2x) where I_o is the zeroth modified Bessel function of the first kind, i.e., I_o[2*(u*x)^(1/2)] = Sum_{j>=0} u^j/j! * x^j/j!. - Tom Copeland, Dec 07 2007
Row polynomial e.g.f.: exp(x*y)(1+2x). - Tom Copeland, Dec 03 2013
|
|
EXAMPLE
|
First few rows of the triangle:
1;
2, 1;
0, 4, 1;
0, 0, 6, 1;
0, 0, 0, 8, 1;
0, 0, 0, 0, 10, 1;
...
|
|
MATHEMATICA
|
T[n_, k_]:= If[k==n, 1, If[k==n-1, 2*n, 0]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 17 2021 *)
|
|
PROG
|
(Sage)
def A134082(n, k): return 1 if k==n else 2*n if k==n-1 else 0
(Magma)
A134082:= func< n, k | k eq n select 1 else k eq n-1 select 2*n else 0 >;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|