

A289070


a(n) = c(2n1), where c(n+2) = Sum_{k=0..n} binomial(n,k)c(k)c(n+1k) with c(0)=0, c(1)=3.


15



3, 9, 108, 2754, 120528, 8059824, 764365248, 97582435344, 16135857600768, 3354823392632064, 856584985953881088, 263495061361859433984, 96111473403635977310208, 41016996175782988022575104, 20247499012863186836834992128, 11447373157054380028382302439424
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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)).


PROG

(PARI) c0=0; c1=3; nmax = 200;
s=vector(nmax+1)); s[1]=c0; s[2]=c1;
for(m=0, #s3, s[m+3]=sum(k=0, m, binomial(m, k)*s[k+1]*s[m+2k]));
a = vector((nmax+1)\2, i, s[2*i])


CROSSREFS

Sequences for other starting pairs: A000111 (1,1), A289064 (1,1), A289065 (2,1), A289066 (3,1), A289067 (3,1), A289068 (1,2), A289069 (3,2).


KEYWORD

nonn


AUTHOR



STATUS

approved



