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A081924 E.g.f.: exp(3*x)/(1-x)^2. 3
1, 5, 27, 159, 1029, 7353, 58095, 506691, 4860297, 51023277, 583097859, 7215769575, 96210083853, 1375803720801, 21012273704151, 341449444105227, 5883436565417745, 107162594556721749, 2057521815411573483 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081923

Polynomials in A010027 evaluated at 4. - Ralf Stephan, Dec 15 2004

LINKS

Iain Fox, Table of n, a(n) for n = 0..450 (first 200 terms from Vincenzo Librandi)

FORMULA

E.g.f.: exp(3*x)/(1-x)^2.

Define f_1(x), f_2(x), ... such that f_1(x) = x*e^x, f_{n+1}(x) = (d/dx)(x*f_n(x)), for n=2,3,.... Then a(n-1) = e^{-1/2}*2^n*f_n(1/2). - Milan Janjic, May 30 2008

G.f.: hypergeom([1,2],[],x/(1-3*x))/(1-3*x). - Mark van Hoeij, Nov 08 2011

a(n) + (-n-4)*a(n-1) + 3*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 24 2012

G.f.: 2/x/G(0) - 1/x, where G(k)= 1 + 1/(1 - x*(2*k+2)/(x*(2*k+5) - 1 + x*(2*k+2)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 31 2013

G.f.: G(0)/x - 1/x, where G(k) = 1 + (2*k + 1)*x/(1-3*x - 2*x*(1-3*x)*(k+1)/(2*x*(k+1) + (1-3*x)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 26 2013

E.g.f.: 1/E(0), where E(k) = 1 - 2*x/(1 - x/(x - 2 + 6/(3 - x*(k+1)/E(k+1)))); (continued fraction). - Sergei N. Gladkovskii, Jun 26 2013

G.f.: (Sum_{k>=0} (k!*(x/(1-3*x))^k) - 1)/x = Q(0)/(2*x) - 1/x, where Q(k) = 1 + 1/(1 - x*(k+1)/(x*(k+1) + (1-3*x)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Aug 09 2013

a(n) ~ exp(3) * n! * n. - Vaclav Kotesovec, Oct 05 2013

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[3x]/(1-x)^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 14 2013 *)

PROG

(PARI) x='x+O('x^66); Vec( serlaplace(exp(3*x)/(1-x)^2) ) \\ Joerg Arndt, Aug 15 2013

CROSSREFS

Sequence in context: A101386 A153233 A084076 * A138772 A258789 A082425

Adjacent sequences:  A081921 A081922 A081923 * A081925 A081926 A081927

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 01 2003

STATUS

approved

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Last modified August 20 15:13 EDT 2019. Contains 326152 sequences. (Running on oeis4.)