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 A321329 #14 Nov 16 2018 04:54:42
%S A321329 1,1,0,-3,0,9,0,-81,0,81,0,-167913,0,2187,0,-23731137,0,287811387,0,
%T A321329 -10310604939,0,13761310401,0,-125613568885131,0,3146863577139,0,
%U A321329 -5409187422305481,0,8241860346410471769
%N A321329 One third of the numerators of a Boas-Buck sequence for the triangular Sheffer matrix S2[3,1] = A282629.
%C A321329 The denominators are given in A321330.
%C A321329 The general Boas-Buck type recurrence for lower triangular Sheffer matrices S(n, m) is: S(n, m) = (n!/(n-m))*Sum_{k=m..n-1} (1/k!)*(alpha(n-1-k) + m*beta(n-1-k))*S(k, m), for n >= m + 1 >= 1, and inputs S(n, n).
%C A321329 See the Boas-Buck type recurrence for the columns of S2[3,1] = A282629.
%C A321329 For S2[3,1] the Boas-Buck sequence alpha is {1, repeat(0)}.
%F A321329 a(n) = (1/3)*numerator(beta(n)), with beta(n) = (-3)^{n+1}* B(n+1)/(n+1)!, where B(n) = A027641(n)/A027642(n) (Bernoulli).
%F A321329 G.f. for rationals {beta(n)}_{n >= 0} is d/dx(log((exp(3*x) - 1)/x)) = (3*x*e^(3*x) - e^(3*x) + 1)/(x*(e^(3*x)-1)).
%e A321329 The rationals beta begin: {3/2, 3/4, 0, -9/80, 0, 27/1120, 0, -243/44800, 0, 243/197120, 0, -503739/1793792000, 0, 6561/102502400, 0, -71193411/4879114240000, 0, 863434161/259568877568000, 0, -30931814817/40789395046400000, 0, ...}.
%t A321329 a[n_] := Numerator[(-3)^(n+1)*BernoulliB[n+1]/(n+1)!/3]; Array[a, 30, 0] (* _Amiram Eldar_, Nov 15 2018 *)
%Y A321329 Cf. A027641/A027642, A282629, A321330.
%K A321329 sign,frac,easy
%O A321329 0,4
%A A321329 _Wolfdieter Lang_, Nov 15 2018