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A001907
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Expansion of e^(-x)/(1-4x).
(Formerly M3112 N1261)
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2
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1, 3, 25, 299, 4785, 95699, 2296777, 64309755, 2057912161, 74084837795, 2963393511801, 130389314519243, 6258687096923665, 325451729040030579, 18225296826241712425, 1093517809574502745499, 69985139812768175711937
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 83.
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.
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 0..350
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FORMULA
| Sum[k=0..n, (-1)^(n+k)*C(n, k)*k!*4^k]. - R. Stephan, May 22 2004
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MATHEMATICA
| With[{nn=20}, CoefficientList[Series[Exp[-x]/(1-4x), {x, 0, nn}], x] Range[0, nn]!] (* or *) Table[Sum[(-1)^(n+k) Binomial[n, k]k! 4^k, {k, 0, n}], {n, 0, 20}](* From Harvey P. Dale, Oct 25 2011 *)
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PROG
| (PARI) a(n)=sum(k=0, n, (-1)^(n+k)*binomial(n, k)*k!*4^k)
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CROSSREFS
| Cf. A000166, A000354, A000180, A001908.
Sequence in context: A126746 A118989 A123989 * A181085 A143635 A023997
Adjacent sequences: A001904 A001905 A001906 * A001908 A001909 A001910
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. Stephan, May 22 2004
Typo fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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