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 A123611 Row sums of triangle A123610. 3

%I

%S 1,2,4,8,20,52,160,492,1620,5408,18504,64132,225440,800048,2865720,

%T 10341208,37568340,137270956,504176992,1860277044,6892335720,

%U 25631327688,95640894056,357975249028,1343650267296,5056424257552

%N Row sums of triangle A123610.

%F a(n) = 2*A047996(2*n,n) = 2*A003239(n) for n>0, where A047996 is the triangle of circular binomial coefficients and A003239(n) = number of rooted planar trees with n non-root nodes.

%F Also equals the row sums of triangle A128545, where A128545(n,k) is the coefficient of q^(n*k) in the q-binomial coefficient [2n,n] for n>=k>=0.

%o (PARI) {a(n)=sum(k=0,n,if(k==0,1,(1/n)*sumdiv(n,d,if(gcd(k,d)==d, eulerphi(d)*binomial(n/d,k/d)^2,0))))}

%Y Cf. A047996, A003239; A123610 (triangle), A123612 (antidiagonal sums); central terms: A123617, A123618.

%Y Cf. A128545.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 03 2006

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Last modified May 24 12:16 EDT 2013. Contains 225620 sequences.