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A002832 Median Euler numbers. 4
1, 3, 24, 402, 11616, 514608, 32394624, 2748340752, 302234850816, 41811782731008, 7106160248346624, 1455425220196234752, 353536812021243273216, 100492698847094242603008, 33045185784774350171111424 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

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 polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26. (In French, with a summary in English on p. 1).

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

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-Fran├žois Alcover, Jul 10 2012, after Maple *)

CROSSREFS

Cf. A000657.

Related polynomials in A098277.

Sequence in context: A145169 A193210 A065761 * A233151 A236466 A185970

Adjacent sequences:  A002829 A002830 A002831 * A002833 A002834 A002835

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

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Last modified November 23 05:04 EST 2014. Contains 249839 sequences.