A117161 -id:A117161 - cp's OEIS frontend

A117166 Column 1 of triangle A117165 of Shift-Moebius coefficients and so equals the Shift-Moebius transform of [1,0,0,0,...].

1, -1, -2, -1, -2, 1, -1, 3, 0, 4, 4, 5, 1, 7, 6, 5, 4, 6, 3, 5, 3, 2, 5, -3, -5, -1, 2, -7, -6, -13, -9, -14, -12, -22, -12, -25, -23, -26, -21, -35, -27, -38, -27, -43, -32, -47, -34, -51, -46, -52, -33, -53, -35, -58, -41, -56, -39, -54, -39, -61, -45, -53, -24, -46, -23, -44, -20, -41, -14, -32, -12, -22

Offset: 1

Wouter Meeussen and Paul D. Hanna, Mar 05 2006

sign

Equals the self-convolution inverse of A117161, which is the limit of columns of triangle A112682.

Cf. A117165 (triangle), A117167 (column 2), A117168 (column 3), A117169 (row sums), A117161 (inverse), A117160, A112682.

{a(n)=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))))[ n,1]}

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

Original entry on oeis.org

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

Wouter Meeussen and Paul D. Hanna, Feb 28 2006

nonn

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...

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

{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]))}

cp's OEIS Frontend

A117166 Column 1 of triangle A117165 of Shift-Moebius coefficients and so equals the Shift-Moebius transform of [1,0,0,0,...].

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