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A161556
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Exponential Riordan array [1 + (sqrt(Pi)/2)*x*exp(x^2/4)*erf(x/2), x].
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4
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1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 2, 0, 6, 0, 1, 0, 10, 0, 10, 0, 1, 6, 0, 30, 0, 15, 0, 1, 0, 42, 0, 70, 0, 21, 0, 1, 24, 0, 168, 0, 140, 0, 28, 0, 1, 0, 216, 0, 504, 0, 252, 0, 36, 0, 1, 120, 0, 1080, 0, 1260, 0, 420, 0, 45, 0, 1
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OFFSET
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0,8
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = [k<=n]*binomial(n,k)*((n-k)/2)!*(1+(-1)^(n-k))/2.
G.f.: 1/(1-x*y-x^2/(1-x*y-x^2/(1-x*y-2x^2/(1-x*y-2x^2/(1-x*y-3x^2/(1-... (continued fraction).
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EXAMPLE
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Triangle begins
1;
0, 1;
1, 0, 1;
0, 3, 0, 1;
2, 0, 6, 0, 1;
0, 10, 0, 10, 0, 1;
6, 0, 30, 0, 15, 0, 1;
0, 42, 0, 70, 0, 21, 0, 1;
24, 0, 168, 0, 140, 0, 28, 0, 1;
Production matrix begins
0, 1;
1, 0, 1;
0, 2, 0, 1;
-1, 0, 3, 0, 1;
0, -4, 0, 4, 0, 1;
6, 0, -10, 0, 5, 0, 1;
0, 36, 0, -20, 0, 6, 0, 1;
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MATHEMATICA
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T[n_, k_] := Boole[k <= n] Binomial[n, k] ((n-k)/2)! (1 + (-1)^(n-k))/2; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 30 2016 *)
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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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