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A146523 Binomial transform of A010685. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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. A029609.

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

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Last modified December 8 20:11 EST 2021. Contains 349596 sequences. (Running on oeis4.)