|
%I #10 Aug 02 2023 07:05:56
%S 1,2,-1,4,-7,14,-91,208,-494,10868,-27170,69160,-535990,1401820,
%T -3704810,29638480,-79653415,215532770,-5280552865,14452039420,
%U -39743108405,329300041070,-913059204785,2540686482880,-21278249294120,59579098023536,-167279775219928,12713262916714528
%N Numerators of coefficients in expansion of (1 + x)^(2/3).
%e (1 + x)^(2/3) = 1 + 2*x/3 - x^2/9 + 4*x^3/81 - 7*x^4/243 + 14*x^5/729 - 91*x^6/6561 + ...
%e Coefficients are 1, 2/3, -1/9, 4/81, -7/243, 14/729, -91/6561, ...
%t nmax = 27; CoefficientList[Series[(1 + x)^(2/3), {x, 0, nmax}], x] // Numerator
%t Table[Binomial[2/3, n], {n, 0, 27}] // Numerator
%o (PARI) my(x='x+O('x^30)); apply(numerator, Vec((1 + x)^(2/3))) \\ _Michel Marcus_, Aug 02 2023
%Y Denominators are A067623.
%Y Cf. A002596, A067622, A127974, A161200, A364661.
%K sign,frac
%O 0,2
%A _Ilya Gutkovskiy_, Aug 01 2023
|
