A166354 Row sums of exponential Riordan array [1+x*tan(x/2),x], A166353.

1, 1, 2, 4, 8, 16, 34, 78, 200, 568, 1806, 6282, 24052, 99100, 443178, 2107966, 10775664, 58092112, 334087750, 2012990930, 12863046636, 85662585604, 602124105122, 4391793687974, 33676375206568, 266989039507576

Offset

0,3

Comments

Binomial transform of aerated Genocchi number variant with e.g.f. 1+x*tan(x/2).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

E.g.f.: exp(x)*(1+x*tan(x/2)).

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

a(n) ~ n! * 2*(exp(Pi)+(-1)^n*exp(-Pi))/Pi^n. - Vaclav Kotesovec, Oct 02 2013

Mathematica

CoefficientList[Series[E^x*(1+x*Tan[x/2]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 02 2013 *)

Crossrefs

Cf. A110501.

Sequence in context: A308245 A209971 A308031 * A336009 A180207 A013025

Adjacent sequences: A166351 A166352 A166353 * A166355 A166356 A166357

Keyword

easy,nonn

Author

Paul Barry, Oct 12 2009

Status

approved