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A131281 Expansion of e.g.f.: 2*(x-1)*tan(x/2+Pi/4)-x^2+2. 2
0, 0, 0, 2, 6, 18, 70, 310, 1582, 9058, 57678, 403878, 3085478, 25535378, 227589206, 2173314806, 22137209694, 239580726978, 2745392996254, 33207657441094, 422813028038230, 5652593799727858, 79168165551184422, 1159200449070638742, 17711278225214739086 (list; graph; refs; listen; history; text; internal format)
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
Essentially the same as 2*A034428.
Sequence in context: A150082 A177470 A060181 * A264036 A261994 A177472
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 30 2007
EXTENSIONS
Definition clarified by Harvey P. Dale, Jun 11 2023
STATUS
approved

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Last modified May 25 03:39 EDT 2024. Contains 372782 sequences. (Running on oeis4.)