This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A284857 #11 Apr 07 2017 04:24:26 %S A284857 1,-1,11,-49,1187,-18083,662407,-3539605,864309187,-949103125, %T A284857 289289620393,-4846044126449,12389144856368069,-69977996793541583, %U A284857 1191089380720588487,-6783915816877925461,3295296805315071712171,-169986671194174827887881,129921413307474873885175559,-149671376459098924087260625 %N A284857 Numerators of the exponential expansion of (3/(log(1+x)))*(1 - 1/(1+x)^(1/3)). %C A284857 For the denominators see A284858. %C A284857 This gives the numerators of the z-sequence for the Sheffer triangle (exp(x), exp(3*x) - 1) shown in A282629. For the notion and use of a- and z- sequences for Sheffer triangles see the W. Lang link under A006232. The a-sequence of this Sheffer triangle is given by A006232/A006233. %C A284857 For the nontrivial decompositions of 1 given by the z-sequence recurrence for the m=0 column repeat(1) of the triangle A282629 see an example there and below. %F A284857 E.g.f.: (3/(log(1+x)))*(1 - 1/(1+x)^(1/3)) for the rational sequence a(n)/A284858(n), n >= 0. %e A284857 The rationals a(n)/A284858(n) start: 1, -1/6, 11/54, -49/108, 1187/810, -18083/2916, 662407/20412, -3539605/17496, 864309187/590490, -949103125/78732, 289289620393/2598156, -4846044126449/4251528, 12389144856368069/967222620, -69977996793541583/446410440, 1191089380720588487/573956280, -6783915816877925461/229582512, ... %e A284857 From the z-recurrence for A282629(5, 0) = 1 one finds: 1 = 5*(1*1 + 255*(-1/6) + 945*(11/54) + 594*(-49/108) + 81*(1187/810)). %Y A284857 Cf. A284858 (denominators), A282629, A006232/A006233. %K A284857 sign,easy %O A284857 0,3 %A A284857 _Wolfdieter Lang_, Apr 04 2017