cp's OEIS Frontend

A067622 Consider the power series (x + 1)^(1/3) = 1 + x/3-x^2/9 + 5x^3/81 + ...; sequence gives numerators of coefficients.

%I A067622 #17 Jul 02 2025 16:02:01
%S A067622 1,1,-1,5,-10,22,-154,374,-935,21505,-55913,147407,-1179256,3174920,
%T A067622 -8617640,70664648,-194327782,537259162,-13431479050,37466757350,
%U A067622 -104906920580,884215473460,-2491879970660,7042269482300,-59859290599550
%N A067622 Consider the power series (x + 1)^(1/3) = 1 + x/3-x^2/9 + 5x^3/81 + ...; sequence gives numerators of coefficients.
%C A067622 a(n) is also the numerator of the binomial coefficient C(k,n) evaluated at k=1/3, e.g. a(4) = (1/24)k(k-1)(k-2)(k-3), plug in k=1/3 and take numerator. - _James R. Buddenhagen_, Aug 16 2014
%F A067622 a(n) =(-1)^n*A004990(n)*A067623(n)/A000244(n); ignoring signs, a(n) =A038502(A004990(n)) =A038502(A034164(n-2)). a(n)'s sign is (-1)^(n+1) if n>0.
%p A067622 s := convert(taylor((x+1)^(1/3), x, 50), polynom): for n from 0 to 50 do printf(`%a,`, abs(numer(coeff(s, x, n)))) od;
%p A067622 seq(numer(subs(k=1/3,expand(binomial(k,n)))),n=0..50) # _James R. Buddenhagen_, Aug 16 2014
%Y A067622 Denominators are A067623.
%K A067622 sign,frac
%O A067622 0,4
%A A067622 _Benoit Cloitre_, Feb 02 2002
%E A067622 Edited by _Henry Bottomley_ and _James Sellers_, Feb 11 2002