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A154556 Exponential Riordan array [exp(-x), x(1+x/2)] 0
1, -1, 1, 1, -1, 1, -1, 0, 0, 1, 1, 2, -3, 2, 1, -1, -5, 5, -5, 5, 1, 1, 9, 0, -5, 0, 9, 1, -1, -14, -21, 35, -35, 21, 14, 1, 1, 20, 70, -56, 35, -56, 70, 20, 1, -1, -27, -162, -42, 189, -189, 42, 162, 27, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Row sums are double factorials A001147 (aerated).

Product A007318*(this triangle) is A122848.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) = (n!/k!)*sum{j=0..k, (-1)^(n-k)*C(k,j)*(-1/2)^j/(n-k-j)!};

T(n,k) = sum{j=0..n, (-1)^(n-j)*C(n,j)*C(j,k)*k!/((2k-j)!*2^(j-k))};

EXAMPLE

Triangle begins

1,

-1, 1,

1, -1, 1,

-1, 0, 0, 1,

1, 2, -3, 2, 1,

-1, -5, 5, -5, 5, 1,

1, 9, 0, -5, 0, 9, 1,

-1, -14, -21, 35, -35, 21, 14, 1,

1, 20, 70, -56, 35, -56, 70, 20, 1,

-1, -27, -162, -42, 189, -189, 42, 162, 27, 1,

1, 35, 315, 510, -735, 693, -735, 510, 315, 35, 1

MATHEMATICA

(* The function RiordanArray is defined in A256893. *)

RiordanArray[E^-#&, # (1 + #/2)&, 10, True] // Flatten (* Jean-Fran├žois Alcover, Jul 19 2019 *)

CROSSREFS

Cf. A001147, A007318, A122848.

Sequence in context: A323834 A082868 A219539 * A260228 A316657 A277914

Adjacent sequences:  A154553 A154554 A154555 * A154557 A154558 A154559

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Jan 11 2009

STATUS

approved

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)