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A002801
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a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2).
(Formerly M1882 N0744)
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4
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1, 1, 2, 8, 50, 418, 4348, 54016, 779804, 12824540, 236648024, 4841363104, 108748223128, 2660609220952, 70422722065040, 2005010410792832, 61098981903602192, 1984186236246187024, 68407835576255308576, 2495374564069015050880, 96019859122742736121376, 3886906732751071879958816, 165120572466718493379680192
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OFFSET
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0,3
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COMMENTS
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Row sums of A152148. [From Paul Barry, Nov 26 2008]
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
J. J. Sylvester, Note on determinants..., Amer. J. Math., 2 (1879), circa p. 94.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..100
E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 223.
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FORMULA
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Appears to be the BinomialMean transform of A007696 (see A075271). - John W. Layman, Oct 01 2002
E.g.f.: exp(x/2)*(1-2*x)^(-1/4). [From Paul Barry, Nov 26 2008]
a(n) = hypergeom([1/4, -n],[],-4)/(2^n) [From Mark van Hoeij, Jun 02 2010]
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PROG
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(Maxima) a(n):=coeff(taylor(exp(x/2)/(1-2*x)^(1/4), x, 0, n), x, n)*n!;
makelist(a(n), n, 0, 12); [Emanuele Munarini, Jul 07 2011]
(PARI) x='x+O('x^66); /* that many terms */
Vec(serlaplace(exp(x/2)*(1-2*x)^(-1/4))) /* show terms */ /* Joerg Arndt, Jul 10 2011 */
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CROSSREFS
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Sequence in context: A120956 A000557 A193352 * A225052 A089104 A050398
Adjacent sequences: A002798 A002799 A002800 * A002802 A002803 A002804
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from John W. Layman, Oct 01 2002
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STATUS
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approved
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