OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..500
EXAMPLE
a(1) = 1*1 =1,
a(2) = 2*1 + 1*1 = 3,
a(3) = 6*1 + 4*1 + 1*3 = 13,
a(4) = 20*1 + 15*1 + 6*3 + 1*13 = 66,
a(5) = 70*1 + 56*1 + 28*3 + 8*13 + 1*66 = 380.
This sequence can be generated by the addition table:
(1)_1__1___1___1 ...
_1__2_(3)__4___5___6 ...
_3__4__6___9_(13)_18__24 ...
13_16_20__26__35__48_(66)_90 ...
66_79_95_115_141_176_224_290_(380) ...
MATHEMATICA
nmax = 30; aa = ConstantArray[0, nmax+1]; aa[[1]] = 1; Do[aa[[n+1]]=Sum[Binomial[2*n-2, n-k-1]*aa[[k+1]], {k, 0, n-1}], {n, 1, nmax}]; aa (* Vaclav Kotesovec, May 06 2015 , much faster than PARI *)
PROG
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(2*n-2, n-k-1)*a(k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 25 2005
STATUS
approved