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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Riordan square is defined in A321620.

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

[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-Fran├žois 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

Adjacent sequences:  A321627 A321628 A321629 * A321631 A321632 A321633

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Dec 09 2018

STATUS

approved

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)