A173612 Odd bisection of A173610.

1, 4, 25, 144, 1024, 7396, 51076, 345744, 2547216, 19114384, 145564225, 1111822336, 8343726336, 62292173056, 459542986816, 3371072258304, 25398293867584, 192578234089536, 1474993183809600, 11338593510740224

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

Example

G.f.: A(x) = 1 + 4*x + 25*x^2 + 144*x^3 + 1024*x^4 + 7396*x^5 +...
Describe the g.f. of A173610 by:
B(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 60*x^6 + 144*x^7 +...
then the g.f. of A173611 is given by C(x) = B(x)^2:
C(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 32*x^4 + 86*x^5 +...
where the square of the coefficients of C(x) form this sequence
and yields the odd bisection of A173610.

Prog

(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}

Crossrefs

Cf. A173610, A173611, A173613.

Sequence in context: A301836 A275177 A079291 * A349540 A072221 A302064

Adjacent sequences: A173609 A173610 A173611 * A173613 A173614 A173615

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2010

Status

approved