A117160 Column 1 of triangle A112682; also equals row sums of A112682 (with offset).

1, 1, 2, 4, 9, 19, 43, 94, 210, 464, 1035, 2295, 5111, 11352, 25259, 56145, 124888, 277669, 617554, 1373201, 3053883, 6790995, 15102178, 33583784, 74684504, 166082706, 369337117, 821331578, 1826484804, 4061741926, 9032530513

Offset: 1

Author

Wouter Meeussen and Paul D. Hanna, Feb 28 2006

Keywords

• nonn

Comments

G.f.: A(x) = g.f. of A117169 (Shift-Moebius[1,1,1,1,...]) divided by the g.f. of A117166 (Shift-Moebius[1,0,0,0,...]) (see A117165 for the Shift-Moebius transform coefficients).

Limit_{n->oo} a(n+1)/a(n) = 2.223805416529545241557...

Crossrefs

Cf. A112682, A117165 (Shift-Moebius), A117169, A117166, A117161.

Programs

PARI

{a(n)=if(n<1,0,SM=prod(i=0,n,matrix(n,n,r,c,if(r>=c, if((r+n-i)%(c+n-i)==0,moebius((r+n-i)/(c+n-i)),0)))); U=SM*vector(n,i,1)~;V=SM*vector(n,i,if(i==1,1,0))~; return(Vec(Ser(U)/Ser(V))[n]))}