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A161556 Exponential Riordan array [1+(sqrt(Pi)/2)*x*exp(x^2/4)*ERF(x/2),x]. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are A084261.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

T(n,k) = [k<=n]*C(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).

EXAMPLE

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;

MATHEMATICA

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-Fran├žois Alcover, Sep 30 2016 *)

CROSSREFS

Cf. A155856, A156367.

Sequence in context: A100749 A124027 A097610 * A317302 A242869 A224878

Adjacent sequences:  A161553 A161554 A161555 * A161557 A161558 A161559

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jun 13 2009

STATUS

approved

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Last modified September 18 05:32 EDT 2019. Contains 327165 sequences. (Running on oeis4.)