A138209 -id:A138209 - cp's OEIS frontend

A138208 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-2n+1))...)^-5)^-3)^-1.

1, 1, -1, 4, -28, 281, -3684, 59731, -1154936, 25950691, -664613080, 19112126640, -609797430996, 21378439099625, -816913146902756, 33793354034365895, -1504592807223959688, 71739597692510725317, -3647111535920547933017

Offset: 0

Paul D. Hanna, Mar 06 2008

sign

			G.f.: A(x)=1+x/B(x), B(x)=1+x/C(x)^3, C(x)=1+x/D(x)^5, D(x)=1+x/E(x)^7, ...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,-1,4,-28,281,-3684,59731,-1154936,25950691,...];
B=[1,1,-3,21,-220,3015,-50721,1009311,-23180763,603647340,...];
C=[1,1,-5,50,-700,12250,-254086,6060285,-163013950,4877935870,...];
D=[1,1,-7,91,-1596,34062,-843003,23549442,-730039689,24824392005,...];
E=[1,1,-9,144,-3036,76527,-2204136,70735467,-2490112548,95152481622,...];
F=[1,1,-11,209,-5148,149721,-4923061,178674925,-7052351735,...]; ...

Cf. A121587, A138211, A138210, A138209.

{a(n)=my(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x/A^(2*(n-j)-1)); polcoeff(A, n)}

A138210 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-2n) )...)^-6)^-4)^-2.

Original entry on oeis.org

1, 1, -2, 11, -96, 1137, -16972, 305653, -6449876, 156135481, -4266372138, 129918213186, -4363433172488, 160251326396727, -6389255111157990, 274851082201092530, -12689236310679318864, 625827924636908620381, -32839089116018960634852

Offset: 0

Paul D. Hanna, Mar 06 2008

sign

			G.f.: A(x)=1+x/B(x)^2, B(x)=1+x/C(x)^4, C(x)=1+x/D(x)^6, D(x)=1+x/E(x)^8,...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,-2,11,-96,1137,-16972,305653,-6449876,156135481,...];
B=[1,1,-4,34,-416,6487,-121740,2660394,-66258116,1852007663,...];
C=[1,1,-6,69,-1088,21126,-480360,12432418,-359714328,11490821943,...];
D=[1,1,-8,116,-2240,52130,-1395592,41877192,-1385795096,50020840015,...];
E=[1,1,-10,175,-4000,108575,-3348372,114475615,-4273407500,...];
F=[1,1,-12,246,-6496,201537,-7039284,270347826,-11252124732,...]; ...

Cf. A121587, A138212, A138209, A138208.

{a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(-2*(n-j))); polcoeff(A, n)}

cp's OEIS Frontend

A138208 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-2n+1))...)^-5)^-3)^-1.

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A138210 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-2n) )...)^-6)^-4)^-2.

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cp's OEIS Frontend

A138208 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(-2n+1))...)^-5)^-3)^-1.

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A138210 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(-2n) )...)^-6)^-4)^-2.

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Author

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Examples

Crossrefs

Programs

PARI

A138208 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-2n+1))...)^-5)^-3)^-1.

A138210 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-2n) )...)^-6)^-4)^-2.