OFFSET
0,5
COMMENTS
Here, i is the imaginary unit. The complex integer sequence c(n) = A289082(n) + i*A289083(n) is one of a family of sequences whose e.g.f.s satisfy the differential equation f''(z) = f'(z)f(z). Each such sequence is uniquely characterized by its two starting terms, which may also be complex integers. For more details, see A289064.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..200
S. Sykora, Sequences related to the differential equation f'' = af'f, Stan's Library, Vol. VI, Jun 2017.
FORMULA
E.g.f.: real(2*L0*tan(L0*z + L1)), where L0 = sqrt(i/2-1/4) and L1 = arccos(sqrt(i/2+1)).
MATHEMATICA
a[0]=1; a[1]=I; a[n_]:=a[n]=Sum[Binomial[n - 2, k] a[k] a[n - 1 - k], {k, 0, n - 2}]; Re[Table[a[n], {n, 0, 50}]] (* Indranil Ghosh, Jul 20 2017 *)
PROG
(PARI) c0=1; c1=I; nmax = 200;
a=vector(nmax+1); a[1]=c0; a[2]=c1;
for(m=0, #a-3, a[m+3]=sum(k=0, m, binomial(m, k)*a[k+1]*a[m+2-k]));
real(a)
CROSSREFS
KEYWORD
sign
AUTHOR
Stanislav Sykora, Jul 19 2017
STATUS
approved