OFFSET
1,2
COMMENTS
There are two kinds of Euler median numbers, the 'right' median numbers (this sequence), and the 'left' median numbers (A000657).
Apparently all terms (except the initial 1) have 3-valuation 1. - F. Chapoton, Aug 02 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
Ange Bigeni and Evgeny Feigin, Symmetric Dellac configurations, arXiv:1808.04275 [math.CO], 2018.
Kwang-Wu Chen, An Interesting Lemma for Regular C-fractions, J. Integer Seqs., Vol. 6, 2003.
D. Dumont, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math., 16 (1995), 275-296.
A. Randrianarivony and J. Zeng, Une famille de polynômes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26. (In French, with a summary in English on p. 1).
R. C. Read, Letter to N. J. A. Sloane, 1992
FORMULA
G.f.: Sum_{n>=0} a(n)*x^n = 1/(1-1*3x/(1-1*5x/(1-2*7x/(1-2*9x/(1-3*11x/...))))).
G.f.: -1/G(0) where G(k)= x*(8*k^2+8*k+3) - 1 - (4*k+5)*(4*k+3)*(k+1)^2*x^2/G(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Aug 08 2012
a(n) ~ 2^(4*n+3/2) * n^(2*n-1/2) / (exp(2*n) * Pi^(2*n-1/2)). - Vaclav Kotesovec, Apr 23 2015
MAPLE
rr := array(1..40, 1..40):rr[1, 1] := 0:for i from 1 to 39 do rr[i+1, 1] := (subs(x=0, diff((exp(x)-1)/cosh(x), x$i))):od: for i from 2 to 40 do for j from 2 to i do rr[i, j] := rr[i, j-1]-rr[i-1, j-1]:od:od: seq(rr[2*i-1, i-1], i=2..20); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu) Feb 16 2001, corrected by R. J. Mathar, Dec 22 2010
MATHEMATICA
max = 20; rr[1, 1] = 0; For[i = 1, i <= 2*max - 1, i++, rr[i + 1, 1] = D[(Exp[x] - 1)/Cosh[x], {x, i}] /. x -> 0]; For[i = 2, i <= 2*max, i++, For[j = 2, j <= i, j++, rr[i, j] = rr[i, j - 1] - rr[i - 1, j - 1]]]; Table[(-1)^i*rr[2*i - 1, i - 1], {i, 2, max}] (* Jean-François Alcover, Jul 10 2012, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 11 1996
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 16 2001
Terms corrected by R. J. Mathar, Dec 22 2010
STATUS
approved