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

0,7

Links

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

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A010892.

Sequence in context: A006490 A307856 A171160 * A306334 A036649 A345322

Adjacent sequences: A139794 A139795 A139796 * A139798 A139799 A139800

Keyword

nonn

Author

Paul Curtz, May 22 2008

Extensions

Edited by R. J. Mathar, Sep 08 2009

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

Status

approved