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.
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +`if`(i>n, 0, b(n-i, i-1)*ithprime(i))))
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i$2)*a(i$2), i=0..n-1))
end:
seq(a(n), n=0..40); # Alois P. Heinz, Jun 13 2018
nmax = 33; CoefficientList[Series[Product[1/(1 + Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 33; CoefficientList[Series[Exp[Sum[Sum[(-1)^k Prime[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (-Prime[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 33}]
N:= 20: # for a(1)..a(N) P:= 1: a:= Vector(N): for n from 1 to N do c:= coeff(P,x,n); if isprime(n) then a[n]:= 1-c else a[n]:= -c fi; P:= series(P/(1-a[n]*x^n),x,N+1); od: convert(a,list); # Robert Israel, Mar 01 2022
A[m_, n_] := A[m, n] = Which[m == 1, Prime[n + 1], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 29]
A[m_, n_] := A[m, n] = Which[m == 1, If[n == 1, 1, Prime[n - 1]], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 55]
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