A173613 Even bisection of A173610.

1, 2, 10, 60, 384, 2752, 19436, 132888, 938448, 6977712, 52748180, 402295360, 3045774336, 22798000896, 169191995264, 1244649595008, 9253079696256, 69936818500032, 532964898123840, 4089541311972480, 31558707924799104

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Example

G.f.: A(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 384*x^4 + 2752*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 product of adjacent coefficients of C(x) form this sequence
and yields the even 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))); if(n==0, 1, polcoeff(A^2, n)*polcoeff(A^2, n-1))}

Crossrefs

Cf. A173610, A173611, A173612.

Sequence in context: A026161 A025188 A114620 * A341924 A350665 A004981

Adjacent sequences: A173610 A173611 A173612 * A173614 A173615 A173616

Keyword

nonn

Author

Paul D. Hanna, Feb 22 2010

Status

approved