VOOZH about

URL: https://oeis.org/A321630

⇱ A321630 - OEIS

login
A321630
The Riordan square of the Euler numbers. Triangle T(n, k), 0 <= k <= n, read by rows.
1
1, 1, 1, 5, 6, 1, 61, 71, 11, 1, 1385, 1532, 162, 16, 1, 50521, 53901, 3638, 278, 21, 1, 2702765, 2821378, 124723, 6504, 419, 26, 1, 199360981, 205440691, 6288561, 218551, 10255, 585, 31, 1, 19391512145, 19825343544, 444121924, 10616960, 340710, 15016, 776, 36, 1
OFFSET
0,4
COMMENTS
The Riordan square is defined in A321620.
Triangle, read by rows, given by [1, 4, 9, 16, 25, 36, 49, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 17 2020
EXAMPLE
Triangle begins:
[0] 1;
[1] 1, 1;
[2] 5, 6, 1;
[3] 61, 71, 11, 1;
[4] 1385, 1532, 162, 16, 1;
[5] 50521, 53901, 3638, 278, 21, 1;
[6] 2702765, 2821378, 124723, 6504, 419, 26, 1;
[7] 199360981, 205440691, 6288561, 218551, 10255, 585, 31, 1;
[8] 19391512145, 19825343544, 444121924, 10616960, 340710, 15016, 776, 36, 1;
MAPLE
# The function RiordanSquare is defined in A321620.
cf := proc(dim) local k, m; m := 1;
for k from dim by -1 to 1 do m := 1 - k^2*x/m od;
1/m end: RiordanSquare(cf(9), 9);
MATHEMATICA
(* The function RiordanSquare is defined in A321620. *)
cf[dim_] := ContinuedFractionK[If[i==1, 1, -(i-1)^2 x], 1, {i, 1, dim}];
RiordanSquare[cf[9], 9] // Flatten (* Jean-François Alcover, Jul 22 2019 *)
CROSSREFS
First column are the Euler numbers A000364.
Row sums are A321631, alternating row sums are A000007.
Cf. A321620.
Sequence in context: A105577 A054655 A290319 * A086745 A086646 A181612
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Dec 09 2018
STATUS
approved