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A321625
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The Riordan square of the swinging factorial (A056040), triangle read by rows, T(n, k) for 0 <= k<= n.
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2
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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
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OFFSET
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0,4
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LINKS
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EXAMPLE
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[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]
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MAPLE
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# The function RiordanSquare is defined in A321620.
SwingingFactorial := (1 + x/(1 - 4*x^2))/sqrt(1 - 4*x^2);
RiordanSquare(SwingingFactorial, 10);
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MATHEMATICA
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(* The function RiordanSquare is defined in A321620. *)
SwingingFactorial = (1 + x/(1 - 4*x^2))/Sqrt[1 - 4*x^2];
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PROG
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(Sage) # uses[riordan_square from A321620]
riordan_square((1 + x/(1 - 4*x^2))/sqrt(1 - 4*x^2), 10)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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