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URL: https://oeis.org/A321625

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A321625
The Riordan square of the swinging factorial (A056040), triangle read by rows, T(n, k) for 0 <= k<= n.
2
1, 1, 1, 2, 3, 1, 6, 10, 5, 1, 6, 22, 22, 7, 1, 30, 66, 66, 38, 9, 1, 20, 140, 218, 146, 58, 11, 1, 140, 372, 574, 542, 270, 82, 13, 1, 70, 826, 1680, 1708, 1134, 446, 110, 15, 1, 630, 1930, 4156, 5432, 4126, 2106, 682, 142, 17, 1
OFFSET
0,4
EXAMPLE
[0] [ 1]
[1] [ 1, 1]
[2] [ 2, 3, 1]
[3] [ 6, 10, 5, 1]
[4] [ 6, 22, 22, 7, 1]
[5] [ 30, 66, 66, 38, 9, 1]
[6] [ 20, 140, 218, 146, 58, 11, 1]
[7] [ 140, 372, 574, 542, 270, 82, 13, 1]
[8] [ 70, 826, 1680, 1708, 1134, 446, 110, 15, 1]
[9] [ 630, 1930, 4156, 5432, 4126, 2106, 682, 142, 17, 1]
MAPLE
# The function RiordanSquare is defined in A321620.
SwingingFactorial := (1 + x/(1 - 4*x^2))/sqrt(1 - 4*x^2);
RiordanSquare(SwingingFactorial, 10);
MATHEMATICA
(* The function RiordanSquare is defined in A321620. *)
SwingingFactorial = (1 + x/(1 - 4*x^2))/Sqrt[1 - 4*x^2];
RiordanSquare[SwingingFactorial, 10] (* Jean-François Alcover, Jun 15 2019, from Maple *)
PROG
(SageMath) # uses[riordan_square from A321620]
riordan_square((1 + x/(1 - 4*x^2))/sqrt(1 - 4*x^2), 10)
CROSSREFS
T(n, 0) = A056040 (swinging factorial), A321626 (row sums), A000007 (alternating row sums).
Cf. A321620.
Sequence in context: A086211 A110189 A187914 * A132372 A103136 A155856
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 22 2018
STATUS
approved