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A002832
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Median Euler numbers.
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7
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1, 3, 24, 402, 11616, 514608, 32394624, 2748340752, 302234850816, 41811782731008, 7106160248346624, 1455425220196234752, 353536812021243273216, 100492698847094242603008, 33045185784774350171111424
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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See related polynomials in A098277.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 16 2001
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STATUS
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approved
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