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A166353 Exponential Riordan array [1+x*tan(x/2),x]. 2
1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 1, 0, 6, 0, 1, 0, 5, 0, 10, 0, 1, 3, 0, 15, 0, 15, 0, 1, 0, 21, 0, 35, 0, 21, 0, 1, 17, 0, 84, 0, 70, 0, 28, 0, 1, 0, 153, 0, 252, 0, 126, 0, 36, 0, 1, 155, 0, 765, 0, 630, 0, 210, 0, 45, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

First column is aerated Genocchi number variant with e.g.f. 1+x*tan(x/2).

Row sums are A166354. Diagonal sums are A166355.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,k) = [k<=n]*G((n-k)/2)*C(n,k)*(1+(-1)^(n-k))/2 where

G(n)=0^n+2(-1)^n*(1-4^n)*sum{k=0..2n, sum{j=0..k, (-1)^j*C(k,j)*j^(2n)/(k+1)}}.

EXAMPLE

Triangle begins

1,

0, 1,

1, 0, 1,

0, 3, 0, 1,

1, 0, 6, 0, 1,

0, 5, 0, 10, 0, 1,

3, 0, 15, 0, 15, 0, 1,

0, 21, 0, 35, 0, 21, 0, 1,

17, 0, 84, 0, 70, 0, 28, 0, 1,

0, 153, 0, 252, 0, 126, 0, 36, 0, 1,

155, 0, 765, 0, 630, 0, 210, 0, 45, 0, 1

MATHEMATICA

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

RiordanArray[1 + # Tan[#/2]&, #&, 11, True] // Flatten (* Jean-Fran├žois Alcover, Jul 19 2019 *)

CROSSREFS

Cf. A110501, A166354, A166355.

Sequence in context: A230427 A229995 A119467 * A110235 A036856 A036855

Adjacent sequences:  A166350 A166351 A166352 * A166354 A166355 A166356

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 12 2009

STATUS

approved

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Last modified October 1 01:28 EDT 2022. Contains 357134 sequences. (Running on oeis4.)