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 A192456 #15 Feb 24 2019 21:09:52
%S A192456 1,1,1,-1,1,-1,1,-2,2,1,-5,1,1,-1,3,-8,1,-7,14,-4,1,-4,4,-64,8,1,-3,9,
%T A192456 -8,12,1,-5,7,-40,20,-32,1,-11,44,-44,44,-16,1,-2,18,-64,4,-192,6112
%N A192456 Numerators in triangle that leads to the Bernoulli numbers.
%C A192456 For the denominators and detailed information see A191302.
%p A192456 nmax:=14: mmax:=nmax: A164555:=proc(n): if n=1 then 1 else numer(bernoulli(n)) fi: end: A027642:=proc(n): if n=1 then 2 else denom(bernoulli(n)) fi: end: for m from 0 to 2*mmax do T(0,m):=A164555(m)/A027642(m) od: for n from 1 to nmax do for m from 0 to 2*mmax do T(n,m):=T(n-1,m+1)-T(n-1,m) od: od: seq(T(n,n+1),n=0..nmax): for n from 0 to nmax do ASPEC(n,0):=2: for m from 1 to mmax do ASPEC(n,m):= (2*n+m)*binomial(n+m-1,m-1)/m od: od: for n from 0 to nmax do seq(ASPEC(n,m),m=0..mmax) od: for n from 0 to nmax do for m from 0 to 2*mmax do SBD(n,m):=0 od: od: for m from 0 to mmax do for n from 2*m to nmax do SBD(n,m):= T(m,m+1) od: od: for n from 0 to nmax do seq(SBD(n,m), m= 0..mmax/2) od: for n from 0 to nmax do BSPEC(n,2) := SBD(n,2)*ASPEC(2,n-4) od: for m from 0 to mmax do for n from 0 to nmax do BSPEC(n,m) := SBD(n,m)*ASPEC(m,n-2*m) od: od: for n from 0 to nmax do seq(BSPEC(n,m), m=0..mmax/2) od: seq(add(BSPEC(n, k), k=0..floor(n/2)) ,n=0..nmax): Tx:=0: for n from 0 to nmax do for m from 0 to floor(n/2) do a(Tx):= numer(BSPEC(n,m)): Tx:=Tx+1: od: od: seq(a(n),n=0..Tx-1); # _Johannes W. Meijer_, Jul 02 2011
%t A192456 (* a=ASPEC, b=BSPEC *) nmax = 13; a[n_, 0] = 2; a[n_, m_] := (2n+m)*Binomial[n+m-1, m-1]/m; b[n_] := BernoulliB[n]; b[1]=1/2; bb = Table[b[n], {n, 0, nmax}]; diff = Table[ Differences[bb, n], {n, 1, nmax}]; dd = Diagonal[diff]; sbd[n_, m_] := If[n >= 2m, -dd[[m+1]], 0]; b[n_, m_] := sbd[n, m]*a[m, n-2m]; Table[b[n, m], {n, 0, nmax}, {m, 0, Floor[n/2]}] // Flatten // Numerator (* _Jean-François Alcover_, Aug 09 2012 *)
%Y A192456 Cf. A191302 (denominators).
%K A192456 sign,frac,tabf
%O A192456 0,8
%A A192456 _Paul Curtz_, Jul 01 2011
%E A192456 Edited and Maple program added by _Johannes W. Meijer_, Jul 02 2011