A155105 Positive numbers appearing in the third column of A155103.

1, 4, 28, 364, 9100, 445900, 43252300, 8347693900, 3213862151500, 2471459994503500, 3798634011551879500, 11673202317498925703500

Offset: 1

Author

Mats Granvik, Jan 20 2009

Keywords

• nonn
• more

Crossrefs

Cf. A155103.

Programs

Maple

A155102 := proc(n,k) if n = k then 1 ; elif n =2*k then -k-1 ; else 0; end if; end proc:
A155103 := proc(amx) a := array(1..amx,1..amx) ; a[1,1] := 1/A155102(1,1) ;
        for r from 1 to amx do
                for c from 1 to r-1 do a[c,r] := 0 ; end do:
                a[r,r] := 1/A155102(r,r) ;
                for c from r-1 to 1 by -1 do a[r,c] := -add(a[cp,c]*A155102(r,cp),cp=c..r-1)/A155102(r,r) ;
                        if c = 3 and a[r,c] <> 0 then print( a[r,c]) ; end if;
                end do:
        end do:
        return ;
end proc:
A155103(290) ; # R. J. Mathar, Dec 07 2010

PARI

\\ after R. J. Mathar
T(n,k)=if(n==k,1,if(n==2*k,-(k+1))); \\ from A155102
\\ First term = 1 omitted
a155103(upto) = my(m=3*2^upto, a=matid(m)); for(r=1, m, forstep(c=r-1, 1, -1, a[r,c]=-sum(cp=c, r-1, a[cp,c]*T(r,cp)); if(c==3 && a[r,c]!=0, print1(a[r,c],", "))));
a155103(8) \\ Hugo Pfoertner, Oct 03 2024

Formula

From Tristan Cam, Oct 02 2024: (Start)

a(1) = 1, a(n) = a(n-1)*(1+3*2^(n-2)) (conjectured).

a(n) = Product_{k=1..n-1} 1+3*2^(k-1) = QPochhammer[-3, 2, n-1]. (conjectured). (End)

Extensions

Two more terms from R. J. Mathar, Dec 07 2010

a(8)-a(12) from Hugo Pfoertner, Oct 02 2024