A166353 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A166353

Exponential Riordan array [1+x*tan(x/2),x].

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

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-François 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