A158120 Unsigned bisection of A157304 and A157305.

1, 2, 26, 1378, 141202, 22716418, 5218302090, 1619288968386, 653379470919714, 333014944014777730, 209463165121436380282, 159492000935562428176162, 144654795258284936534929586, 154140229756873813307283828098

Offset: 0

Author

Paul D. Hanna, Mar 12 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 26*x^2 + 1378*x^3 + 141202*x^4 +...
RELATED FUNCTIONS.
G.f. of A157305, B(x) = x + A(-x^2), satisfies the condition
that both B(x) and F(x) = B(x*F(x)^2) = o.g.f. of A157307
have zeros for every other coefficient after initial terms:
A157305 = [1,1,-2,0,26,0,-1378,0,141202,0,-22716418,0,...];
A157307 = [1,1,0,-7,0,242,0,-17771,0,2189294,0,-404590470,0,...].
...
G.f. of A157304, C(x) = 2+x - A(-x^2), satisfies the condition
that both C(x) and G(x) = C(x/G(x)^2) = o.g.f. of A157302
have zeros for every other coefficient after initial terms:
A157308 = [1,1,2,0,-26,0,1378,0,-141202,0,22716418,0,...];
A157302 = [1,1,0,-5,0,183,0,-14352,0,1857199,0,-355082433,0,...].
...
		

Links

• Paul D. Hanna, Table of n, a(n) for n=0..50

Crossrefs

Cf. A157304, A157305, A157302, A157307, A158119.

Programs

PARI

{a(n)=local(A=[1, 1]); for(i=1, 2*n, if(#A%2==0, A=concat(A, t); A[ #A]=-subst(Vec(serreverse(x/Ser(A)))[ #A], t, 0)); if(#A%2==1, A=concat(A, t); A[ #A]=-subst(Vec(x/serreverse(x*Ser(A)))[ #A], t, 0))); (-1)^n*Vec(x/serreverse(x*Ser(A)))[2*n+1]}