OFFSET
1,1
COMMENTS
The sequence c(n) is one of a family of integer sequences whose e.g.f.s satisfy the differential equation f''(z) = f'(z)f(z).
Since c(0)=0, all its even terms are zero, and only the odd terms are listed here. For more details, see A289064 and the link.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..100
S. Sykora, Sequences related to the differential equation f'' = af'f, Stan's Library, Vol. VI, Jun 2017.
FORMULA
E.g.f.: odd terms of sqrt(6)*tan(z*sqrt(3/2)).
E.g.f. for (-1)^(n)*a(n): odd terms of -sqrt(6)*tanh(z*sqrt(3/2)).
a(n) ~ (2n-1)! * 2^(n+2) * 3^n / Pi^(2*n). - Vaclav Kotesovec, Jun 24 2017
PROG
(PARI) c0=0; c1=3; nmax = 200;
s=vector(nmax+1)); s[1]=c0; s[2]=c1;
for(m=0, #s-3, s[m+3]=sum(k=0, m, binomial(m, k)*s[k+1]*s[m+2-k]));
a = vector((nmax+1)\2, i, s[2*i])
CROSSREFS
KEYWORD
nonn
AUTHOR
Stanislav Sykora, Jun 23 2017
STATUS
approved