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 A174263 #8 Jan 12 2019 20:02:51
%S A174263 0,1,-5,14,-23,349,-499,793,-1038,7901,-9791,65488,-78193,795259,
%T A174263 -925389,1615811,-1841036,67142767,-75821437,358067518,-388783203,
%U A174263 -521129621,480390923,133108162049
%N A174263 Numerator of the n-th term of the inverse Binomial Transform of the Bernoulli sequence prefixed with 0.
%C A174263 The inverse binomial transform of 0, 1, -1/2, 1/6, 0, ... is A(n) = 0, 1, -5/2, 14/3, -23/3, ... The current sequence is defined by the numerators; the denominators are A100650(n).
%C A174263 There is a connection to the sequence b(n) = 0, 1, 1/2, 1/6, 0, -1/30, ... of modified Bernoulli numbers [b(0)=0, b(2) = -Bernoulli(1), b(n) = Bernoulli(n-1) if n <> 2] discussed in A165142: The inverse binomial transform of b(n) is c(n) = 0, 1, -3/2, 5/3, -5/3, 49/30, -49/30, ..., and c(n) - A(n) = (-1)^n*A000217(n-1).
%p A174263 read("transforms") ;
%p A174263 A174264 := proc(n) local b; b := [0,seq(bernoulli(i),i=0..n+1)] ; BINOMIALi(b) ; numer(op(n+1,%)) ; end proc:
%p A174263 seq(A174264(n),n=0..30) ; # _R. J. Mathar_, Jan 21 2011
%Y A174263 Cf. A164558.
%K A174263 sign,frac
%O A174263 0,3
%A A174263 _Paul Curtz_, Mar 14 2010