A138210 -id:A138210 - 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)}

A138209 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-3n) )...)^-9)^-6)^-3.

Original entry on oeis.org

1, 1, -3, 24, -307, 5367, -118836, 3185098, -100249284, 3625011513, -148109085520, 6748573217802, -339316619619180, 18662532511884138, -1114624766173882896, 71841450181505629686, -4970296376217834343751, 367389368833834570991097

Offset: 0

Paul D. Hanna, Mar 06 2008

sign

			G.f.: A(x)=1+x/B(x)^3, B(x)=1+x/C(x)^6, C(x)=1+x/D(x)^9, D(x)=1+x/E(x)^12, ...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,-3,24,-307,5367,-118836,3185098,-100249284,...];
B=[1,1,-6,75,-1352,31167,-867294,28172631,-1044977994,...];
C=[1,1,-9,153,-3567,102591,-3461832,133195605,-5737614804,...];
D=[1,1,-12,258,-7384,254955,-10139508,452535442,-22298633472,...];
E=[1,1,-15,390,-13235,533700,-24472908,1245207030,-69239330640,...];
F=[1,1,-18,549,-21552,994392,-51685074,2955896076,-183324843810,...]; ...

Cf. A121587, A138213, A138210, A138208.

{a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(-3*(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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A138209 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-3n) )...)^-9)^-6)^-3.

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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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A138209 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(-3n) )...)^-9)^-6)^-3.

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Author

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Examples

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Programs

PARI

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

A138209 G.f.: A(x) = 1 + x(1 + x(1 + x(...(1 + x(...)^(-3n) )...)^-9)^-6)^-3.