A139797 Inverse binomial transform of [0, A133474].

0, 0, 0, 0, 1, 1, 3, 4, 10, 18, 39, 75, 153, 302, 608, 1212, 2429, 4853, 9711, 19416, 38838, 77670, 155347, 310687, 621381, 1242754, 2485516, 4971024, 9942057, 19884105, 39768219, 79536428, 159072866, 318145722, 636291455, 1272582899, 2545165809, 5090331606, 10180663224, 20361326436, 40722652885, 81445305757

Offset: 0

Author

Paul Curtz, May 22 2008

Keywords

• nonn

Links

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

Crossrefs

Cf. A010892.

Programs

Magma

f:= func< n | Evaluate(ChebyshevU(n+1), 1/2) >;
[n eq 0 select 0 else ((3*n-4)*(-1)^n +2^n +3*f(n) -6*f(n-1))/27: n in [0..60]]; // G. C. Greubel, Mar 08 2021

Mathematica

Table[((3*n-4)*(-1)^n +2^n +3*ChebyshevU[n, 1/2] -6*ChebyshevU[n-1, 1/2])/27, {n, 0, 60}] (* G. C. Greubel, Mar 08 2021 *)

Sage

[( (3*n-4)*(-1)^n +2^n +3*chebyshev_U(n, 1/2) -6*chebyshev_U(n-1, 1/2) )/27 for n in (0..60)] # G. C. Greubel, Mar 08 2021

Formula

G.f.: x^4/((1+x)^2 * (1-2*x) * (1-x+x^2)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

a(n) = ( (3*n-4)*(-1)^n +2^n +3*ChebyshevU(n, 1/2) -6*ChebyshevU(n-1, 1/2) )/27. - G. C. Greubel, Mar 08 2021

Extensions

Edited by R. J. Mathar, Sep 08 2009

Terms a(29) onward added by G. C. Greubel, Mar 08 2021