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 A082032 Expansion of e.g.f.: exp(2*x)/(1-2*x). 5
 1, 4, 20, 128, 1040, 10432, 125248, 1753600, 28057856, 505041920, 10100839424, 222218469376, 5333243269120, 138664325005312, 3882601100165120, 116478033004986368, 3727297056159629312, 126728099909427527680, 4562211596739391258624, 173364040676096868352000, 6934561627043874735128576 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A010844. a(n) = b such that Integral_{x=0..1} (2*x)^n*exp(-x) dx = c - b*exp(-1). - Francesco Daddi, Jul 31 2011 LINKS 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. FORMULA E.g.f.: exp(2*x)/(1-2*x) a(n) = 2^n*A000522(n). - Vladeta Jovovic, Oct 29 2003 a(n) = 2n*a(n)+2^n, n>0, a(0)=1. - Paul Barry, Aug 26 2004 a(n) +2*(-n-1)*a(n-1) +4*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 26 2012 G.f.: 1/Q(0), where Q(k)= 1 - 2*x - 2*x*(k+1)/(1-2*x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 19 2013 G.f.: 1/Q(0), where Q(k) = 1 - 4*x*(k+1) - 4*x^2*(k+1)^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Sep 30 2013 a(n) = 2^n*hypergeometric_U(1,n+2,1). - Peter Luschny, Nov 26 2014 MATHEMATICA With[{nn=30}, CoefficientList[Series[Exp[2x]/(1-2x), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 02 2021 *) PROG (PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(2*x)/(1-2*x))) \\ Michel Marcus, Jan 27 2019 CROSSREFS Cf. A000522, A010844, A082033. Sequence in context: A080795 A126674 A196557 * A140585 A132436 A307006 Adjacent sequences:  A082029 A082030 A082031 * A082033 A082034 A082035 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 02 2003 EXTENSIONS More terms from Michel Marcus, Jan 27 2019 STATUS approved

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Last modified September 25 18:49 EDT 2021. Contains 347659 sequences. (Running on oeis4.)