A117161 - OEIS

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

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OFFSET

1,3

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

FORMULA

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

PROG

(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]))}

CROSSREFS

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

Sequence in context: A097941 A317792 A293732 * A319765 A244707 A244708

Adjacent sequences: A117158 A117159 A117160 * A117162 A117163 A117164

KEYWORD

nonn

AUTHOR

Wouter Meeussen and Paul D. Hanna, Feb 28 2006

STATUS

approved