A370480 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/3) / (1-x))^2 )^3.
1, 3, 15, 73, 360, 1800, 9112, 46632, 240936, 1255336, 6589080, 34811784, 184990568, 988156872, 5303039256, 28579068520, 154605138984, 839272725864, 4570409517848, 24961191298248, 136688674353000, 750355591919240, 4128471397725336, 22762905189252264
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec((1+x*((1-x-sqrt(1-6*x+x^2))/(2*x))^2)^3) -
PARI
a(n, r=3, s=2, t=2, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
Formula
G.f.: B(x)^3 where B(x) is the g.f. of A006319.
a(n) = 3 * Sum_{k=0..n} binomial(2*k+3,k) * binomial(n+k-1,n-k)/(2*k+3).