login
A139797
Inverse binomial transform of [0, A133474].
2
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
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
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