OFFSET
0,4
LINKS
Y. Sano, The principal numbers of K. Saito for the types A_l, D_l and E_l, Discr. Math., 307 (2007), 2636-2642.
FORMULA
E.g.f. E(x)=2*(x-1)*tan(x/2+Pi/4)-x^2+2 = 2*x - x^2 + 4*x*(x-1)/(Q(0)-x) where Q(k) = 4*k + 2 - x^2/Q(k+1); (continued fraction, 1-step).- Sergei N. Gladkovskii, Jun 22 2012
a(n) ~ n! * 2^(n + 2) * (Pi - 2) / Pi^(n + 1). - Vaclav Kotesovec, Mar 12 2019
MATHEMATICA
With[{nn=30}, CoefficientList[Series[2(x-1)Tan[x/2+Pi/4]-x^2+2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 11 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 30 2007
EXTENSIONS
Definition clarified by Harvey P. Dale, Jun 11 2023
STATUS
approved