OFFSET
0,1
COMMENTS
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-1) and L1 = arccos(sqrt(i+1)).
MATHEMATICA
a[n_] := a[n] = Which[n == 0, 2, n == 1, 2 I, True, Sum[Binomial[n - 2, k] a[k] a[n - 1 - k], {k, 0, n - 2}]]; Re@ Array[a, 23, 0] (* Michael De Vlieger, Jul 20 2017 *)
PROG
(PARI) c0=2; c1=2*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