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A117161
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Limit of columns of triangle A112682.
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3
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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
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1,3
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COMMENTS
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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...
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LINKS
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FORMULA
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a(n) ~ c * d^n, where d = 2.22380541652954524155773588821857101036961489569496661752400123603526677062... and c = 0.26711638477321148860322250949475835248606998843344097590907725227209181124... - Vaclav Kotesovec, Feb 08 2023
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PROG
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(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]))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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