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A000657
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Median Euler numbers (the middle numbers of Arnold's shuttle triangle).
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5
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1, 1, 4, 46, 1024, 36976, 1965664, 144361456, 13997185024, 1731678144256, 266182076161024, 49763143319190016, 11118629668610842624, 2925890822304510631936, 895658946905031792553984, 315558279782214450517374976
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., 47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51.
V. I. Arnold, Springer numbers and Morsification spaces. J. Algebraic Geom. 1 (1992), no. 2, 197-214.
D. Dumont, Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers, Adv. Appl. Math., 16 (1995), 275-296.
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LINKS
| A. Randrianarivony and J. Zeng, Une famille des polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26.
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FORMULA
| Row sums of triangle, read by rows, [0, 1, 4, 9, 16, 25, 36, 49, ...] DELTA [1, 2, 6, 5, 11, 8, 16, 11, 21, 14, ...] where DELTA is Deleham's operator defined in A084938.
G.f.: Sum[n>=0, a(n)x^n] = 1/(1-1*1x/(1-1*3x/(1-2*5x/(1-2*7x/(1-3*9x/...))))). - R. Stephan, Sep 09 2004
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MAPLE
| Digits := 40: rr := array(1..40, 1..40): rr[1, 1] := 1: for i from 1 to 39 do rr[i+1, 1] := subs(x=0, diff(1+tan(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]-(-1)^i*rr[i-1, j-1]: od: od: [seq(rr[2*i-1, i], i=1..20)];
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CROSSREFS
| Cf. A084938, A002832. For a signed version see A099023.
Related polynomials in A098277.
Sequence in context: A126739 A191870 A099023 * A001623 A002077 A113096
Adjacent sequences: A000654 A000655 A000656 * A000658 A000659 A000660
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), D. E. Knuth
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EXTENSIONS
| More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) Feb 12 2001, corrected by S. A. Irvine, Dec 22 2010
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