A146523 Binomial transform of A010685.

1, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120, 10737418240

Offset

0,2

Comments

Linked to A029609 by a Catalan transform.

Hankel transform is (1, -15, 0, 0, 0, 0, 0, 0, 0, ...).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2).

Formula

a(n) = 5*2^(n-1) for n >= 1, a(0) = 1.

a(n) = Sum_{k=0..n} A109466(n,k)*A029609(k).

a(n) = A084215(n+1) = A020714(n-1), n > 0. - R. J. Mathar, Nov 02 2008

G.f.: (1 + 3*x)/(1 - 2*x). - Vladimir Joseph Stephan Orlovsky, Jun 21 2011

G.f.: G(0), where G(k)= 1 + 3*x/(1 - 2*x/(2*x + 3*x/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 03 2013

E.g.f.: (5*exp(2*x) - 3)/2. - Stefano Spezia, Feb 20 2023

Mathematica

CoefficientList[Series[(1+3x)/(1-2x), {x, 0, 50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)
Join[{1}, 5*2^(Range[40] -1)] (* G. C. Greubel, Nov 23 2021 *)

Prog

(PARI) a(n)=if(n, 5<<(n-1), 1) \\ Charles R Greathouse IV, Jan 17 2012
(Sage) [1]+[5*2^(n-1) for n in (1..50)] # G. C. Greubel, Nov 23 2021

Crossrefs

Cf. A010685, A020714, A029609, A084215, A109466.

Sequence in context: A193839 A323831 A020714 * A102260 A023383 A229171

Adjacent sequences: A146520 A146521 A146522 * A146524 A146525 A146526

Keyword

nonn,easy

Author

Philippe Deléham, Oct 30 2008

Status

approved