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Search: id:A002421
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| A002421 |
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Expansion of (1-4x)^(3/2).
(Formerly M4058 N1683)
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+0
8
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| 1, -6, 6, 4, 6, 12, 28, 72, 198, 572, 1716, 5304, 16796, 54264, 178296, 594320, 2005830, 6843420, 23571780, 81880920, 286583220, 1009864680, 3580429320, 12765008880, 45741281820
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Terms that are not divisible by 12 have indices in A019469. - R. Stephan, Aug 26 2004
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 164.
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 55.
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FORMULA
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a(n) = sum[ m=0..n ] binomial(n, m) K_m(4), where K_m(x)=K_m(n, 2, x) is a Krawtchouk polynomial - abarg(AT)research.bell-labs.com (Alexander Barg).
a(n) ~ 3/4*pi^(-1/2)*n^(-5/2)*2^(2*n)*{1 + 15/8*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 22 2001
For n>1, a(n) = 12 * (2n-4)! / [n!(n-2)! ] = 2(Cat(n-1)-4*Cat(n-2)) = 12*Cat(n-2)/n. Proof: G.f. is (1-4x) times the g.f. of A002420. - R. Stephan, Aug 26 2004
12 * (2n-4)! / [n(n-1)!(n-2)! ], n>1. In terms of Catalan numbers (A000108), a(n) = 12*Cat(n-2)/n. Terms that are not divisible by 12 have indices in A019469. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 11 2004
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CROSSREFS
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Cf. A007054, A004001, A002420, A002422-A002424.
Cf. A000257, A071721, A071724, A085687.
Sequence in context: A019957 A099405 A090966 this_sequence A165953 A045885 A019118
Adjacent sequences: A002418 A002419 A002420 this_sequence A002422 A002423 A002424
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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