cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

1, 1, -1, 4, -28, 281, -3684, 59731, -1154936, 25950691, -664613080, 19112126640, -609797430996, 21378439099625, -816913146902756, 33793354034365895, -1504592807223959688, 71739597692510725317, -3647111535920547933017
Offset: 0

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			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,...]; ...

Crossrefs

Cf. A121587, A138211, A138210, A138209.

Programs

  • PARI
    {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

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			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,...]; ...

Crossrefs

Cf. A121587, A138213, A138210, A138208.

Programs

  • PARI
    {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)}

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

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			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,...]; ...

Crossrefs

Cf. A121587, A138212, A138209, A138208.

Programs

  • PARI
    {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)}

A197772 G.f.: A(x) = 1/(1 - x*B(x)), where B(x) = 1/(1 - x*C(x)^2); C(x) = 1/(1 - x*D(x)^3); D(x) = 1/(1 - x*E(x)^4); ...

Original entry on oeis.org

1, 1, 2, 6, 25, 138, 968, 8313, 84735, 1000322, 13418848, 201526744, 3348677251, 60981586323, 1207531891440, 25829355773719, 593485342700358, 14577731251921826, 381175458103542506, 10570762449548976706, 309889778765890035970, 9575316933047901325098
Offset: 0

Views

Author

Paul D. Hanna, Dec 09 2011

Keywords

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 138*x^5 + 968*x^6 +...
The g.f. A = A(x) is generated by:
A = 1/(1-x*B), B = 1/(1-x*C^2), C = 1/(1-x*D^3), D = 1/(1-x*E^4), E = 1/(1-x*F^5), ...
where the coefficients in the respective power series begin:
B: [1, 1, 3, 14, 87, 672, 6202, 66622, 817205, 11278833, ...];
C: [1, 1, 4, 25, 203, 1989, 22627, 291964, 4206530, 66905338, ...];
D: [1, 1, 5, 39, 389, 4600, 62087, 935506, 15512217, 280252770, ...];
E: [1, 1, 6, 56, 661, 9141, 142642, 2458133, 46147009, 935047405, ...];
F: [1, 1, 7, 76, 1035, 16373, 289864, 5622842, 117940453, 2651283277, ...]; ...
and the coefficients in the indicated powers begin:
C^2: [1, 2, 9, 58, 472, 4584, 51481, 655244, 9318663, ...];
D^3: [1, 3, 18, 148, 1491, 17496, 232556, 3441024, 56009937, ...];
E^4: [1, 4, 30, 300, 3605, 49656, 763968, 12920820, 237676330, ...];
F^5: [1, 5, 45, 530, 7400, 117096, 2048865, 39048150, 802555995, ...]; ...

Crossrefs

Cf. A121587.

Programs

  • PARI
    {a(n)=local(A=1+O(x));for(m=1,n,A=1/(1-x*A^(n-m+1)+x*O(x^n)));polcoeff(A,n)}
Showing 1-4 of 4 results.

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