A370477 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/2) / (1-x))^(3/2) )^2.
1, 2, 7, 24, 83, 290, 1023, 3640, 13052, 47124, 171190, 625328, 2295561, 8464690, 31339455, 116458200, 434217000, 1623971580, 6090823890, 22903571280, 86332453350, 326145976884, 1234662753126, 4682968975664, 17794062340008, 67726620644200
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec((1+x*((1-sqrt(1-4*x))/(2*x))^3)^2) -
PARI
a(n, r=2, s=3/2, t=3/2, 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)^2 where B(x) is the g.f. of A071724.
a(n) = 2 * Sum_{k=0..n} binomial(3*k/2+2,k) * binomial(n+k/2-1,n-k)/(3*k/2+2).