A117161 Limit of columns of triangle A112682.

1, 1, 3, 6, 15, 31, 73, 157, 358, 785, 1762, 3896, 8702, 19299, 42995, 95507, 212552, 472445, 1050973, 2336670, 5197036, 11556157, 25700188, 57150018, 127093805, 282627186, 628514815, 1397684691, 3108193486, 6911996344, 15370966058

Offset: 1

Author

Wouter Meeussen and Paul D. Hanna, Feb 28 2006

Keywords

• nonn

Comments

Equals the self-convolution inverse of A117166, where A117166 is the Shift-Moebius transform of [1,0,0,0,...] (see A117165 for the Shift-Moebius transform coefficients).

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A112682, A117166 (inverse), A117165 (Shift-Moebius).

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)))); RV=SM*vector(n,i,if(i==1,1,0))~;return(Vec(1/Ser(RV))[n]))}

Formula

a(n) ~ c * d^n, where d = 2.22380541652954524155773588821857101036961489569496661752400123603526677062... and c = 0.26711638477321148860322250949475835248606998843344097590907725227209181124... - Vaclav Kotesovec, Feb 08 2023