A161556 Exponential Riordan array [1 + (sqrt(Pi)/2)*x*exp(x^2/4)*erf(x/2), x].

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

Offset: 0

Author

Paul Barry, Jun 13 2009

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A084261.

Examples

			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;
		

Links

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

Crossrefs

Cf. A155856, A156367.

Programs

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-François Alcover, Sep 30 2016 *)

Formula

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).