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 A173613 Even bisection of A173610. 3

%I

%S 1,2,10,60,384,2752,19436,132888,938448,6977712,52748180,402295360,

%T 3045774336,22798000896,169191995264,1244649595008,9253079696256,

%U 69936818500032,532964898123840,4089541311972480,31558707924799104

%N Even bisection of A173610.

%F a(n) = A173611(n)*A173611(n-1) for n>0, with a(0)=1, where A173611 is the self-convolution of A173610.

%e G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 384*x^4 + 2752*x^5 +...

%e Describe the g.f. of A173610 by:

%e B(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 60*x^6 + 144*x^7 +...

%e then the g.f. of A173611 is given by C(x) = B(x)^2:

%e C(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 32*x^4 + 86*x^5 +...

%e where the product of adjacent coefficients of C(x) form this sequence

%e and yields the even bisection of A173610.

%o (PARI) {a(n)=local(A=1+x,B); for(i=1,n,B=(A+x*O(x^n))^2;A=1+x*sum(m=0,n\2,polcoeff(B,m)*polcoeff(B,m+1)*x^(2*m+1)) +x*sum(m=0,n\2,polcoeff(B,m)^2*x^(2*m)));if(n==0,1,polcoeff(A^2,n)*polcoeff(A^2,n-1))}

%Y Cf. A173610, A173611, A173612.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 22 2010

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Last modified October 31 00:25 EDT 2020. Contains 338095 sequences. (Running on oeis4.)