A173612 - OEIS

%I #2 Mar 30 2012 18:37:21

%S 1,4,25,144,1024,7396,51076,345744,2547216,19114384,145564225,

%T 1111822336,8343726336,62292173056,459542986816,3371072258304,

%U 25398293867584,192578234089536,1474993183809600,11338593510740224

%N Odd bisection of A173610.

%F a(n) = A173611(n)^2, where A173611 is the self-convolution of A173610.

%e G.f.: A(x) = 1 + 4*x + 25*x^2 + 144*x^3 + 1024*x^4 + 7396*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 square of the coefficients of C(x) form this sequence

%e and yields the odd 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)));polcoeff(A^2,n)^2}

%Y Cf. A173610, A173611, A173613.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 22 2010