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


%S 1,1,2,4,8,16,34,78,200,568,1806,6282,24052,99100,443178,2107966,

%T 10775664,58092112,334087750,2012990930,12863046636,85662585604,

%U 602124105122,4391793687974,33676375206568,266989039507576

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

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

%H Vincenzo Librandi, <a href="/A166354/b166354.txt">Table of n, a(n) for n = 0..200</a>

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

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

%F 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)}}.

%F a(n) ~ n! * 2*(exp(Pi)+(-1)^n*exp(-Pi))/Pi^n. - _Vaclav Kotesovec_, Oct 02 2013

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

%Y Cf. A110501.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Oct 12 2009

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Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)