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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 12 2009
STATUS
approved