OFFSET
0,4
COMMENTS
The denominators are given in A321330.
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).
See the Boas-Buck type recurrence for the columns of S2[3,1] = A282629.
For S2[3,1] the Boas-Buck sequence alpha is {1, repeat(0)}.
FORMULA
EXAMPLE
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, ...}.
MATHEMATICA
a[n_] := Numerator[(-3)^(n+1)*BernoulliB[n+1]/(n+1)!/3]; Array[a, 30, 0] (* Amiram Eldar, Nov 15 2018 *)
CROSSREFS
KEYWORD
sign,frac,easy
AUTHOR
Wolfdieter Lang, Nov 15 2018
STATUS
approved