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 1-8 of 8 results.

A138211 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, 3, 18, 166, 2070, 32505, 614918, 13600671, 344202033, 9806468970, 310553772735, 10820519947581, 411338412455910, 16940944600551504, 751397442828052440, 35707884976794347170, 1810006747594245718317
Offset: 0

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			G.f.: A(x)=1+x*B(x)^1, 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=[1,1,1,3,18,166,2070,32505,614918,13600671,...];
B=[1,1,3,18,166,2070,32505,614918,13600671,344202033,...];
C=[1,1,5,45,570,9175,177836,4016810,103426120,2987875840,...];
D=[1,1,7,84,1358,26957,626871,16609768,492427321,16126773012,...];
E=[1,1,9,135,2658,62892,1712034,52281819,1762364970,64849739238,...];
F=[1,1,11,198,4598,126456,3950837,136929254,5186142291,212476739640,...];

Crossrefs

Cf. A095793, A138212, A138213, A138214, A138215, A138216.

Programs

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

A138213 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(3n))...)^9)^6)^3.

Original entry on oeis.org

1, 1, 3, 21, 244, 4002, 84909, 2209947, 68121822, 2425846806, 97969327890, 4423628854404, 220806455598561, 12072207455321168, 717431790926502954, 46045783798588216767, 3174068594948910976851, 233875508656473241657578
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=[1,1,3,21,244,4002,84909,2209947,68121822,2425846806,...];
B=[1,1,6,69,1154,25062,665862,20869399,752900220,30714860088,...];
C=[1,1,9,144,3162,86346,2789703,103536696,4329341244,...];
D=[1,1,12,246,6700,221145,8453892,364604520,17444393868,...];
E=[1,1,15,375,12200,472875,20921433,1031067730,55735025670,...];
F=[1,1,18,531,20094,895077,45035802,2500543500,150992211456,...]; ...

Crossrefs

Cf. A095793, A138211, A138212, A138214, A138215, A138216.

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)}

A138214 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(4n))...)^12)^8)^4.

Original entry on oeis.org

1, 1, 4, 38, 596, 13137, 373544, 13008184, 535947320, 25492727304, 1374588760980, 82844371459764, 5518323917106220, 402556752045926108, 31916585459440839392, 2732642735337686840152, 251267557458318511262096
Offset: 0

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			G.f.: A(x)=1+x*B(x)^4, B(x)=1+x*C(x)^8, C(x)=1+x*D(x)^12, D(x)=1+x*E(x)^16,...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,4,38,596,13137,373544,13008184,535947320,25492727304,...];
B=[1,1,8,124,2792,81462,2902528,121830916,5880235184,...];
C=[1,1,12,258,7612,278991,12084552,600710380,33615167976,...];
D=[1,1,16,440,16080,711740,36459968,2105685752,134824193120,...];
E=[1,1,20,670,29220,1517725,89938984,5933795760,429195194520,...];
F=[1,1,24,948,48056,2866962,193128768,14351122716,1159330814736,...]; ...

Crossrefs

Cf. A095793, A138211, A138212, A138213, A138215, A138216.

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(4*(n-j))); polcoeff(A, n)}

A138215 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(5n))...)^15)^10)^5.

Original entry on oeis.org

1, 1, 5, 60, 1185, 32805, 1169626, 51021010, 2631549790, 156635460260, 10566145206715, 796523479440060, 66355853815084855, 6053343246845576335, 600137100011260447750, 64247982820612486908840
Offset: 0

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			G.f.: A(x)=1+x*B(x)^5, B(x)=1+x*C(x)^10, C(x)=1+x*D(x)^15, D(x)=1+x*E(x)^20,...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,5,60,1185,32805,1169626,51021010,2631549790,...];
B=[1,1,10,195,5520,202235,9038502,475490115,28745939090,...];
C=[1,1,15,405,15005,690165,37491378,2335884815,163755375450,...];
D=[1,1,20,690,31640,1756595,112818004,8165592610,654987108920,...];
E=[1,1,25,1050,57425,3739650,277763130,22962379750,2080527807050,...];
F=[1,1,30,1485,94360,7055580,595576506,55444469360,5610038179890,...]; ...

Crossrefs

Cf. A095793, A138211, A138212, A138213, A138214, A138216.

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(5*(n-j))); polcoeff(A, n)}

A138216 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(6n))...)^18)^12)^6.

Original entry on oeis.org

1, 1, 6, 87, 2072, 69051, 2960496, 155190175, 9614870340, 687262107456, 55663739264928, 5037617218937667, 503778146624222544, 55164755650126969274, 6564517420892162939514, 843494176565238712267131
Offset: 0

Views

Author

Paul D. Hanna, Mar 06 2008

Keywords

Examples

			G.f.: A(x)=1+x*B(x)^6, B(x)=1+x*C(x)^12, C(x)=1+x*D(x)^18, D(x)=1+x*E(x)^24,...
where A(x),B(x),C(x),... are the g.f. of the sequences given below.
A=[1,1,6,87,2072,69051,2960496,155190175,9614870340,...];
B=[1,1,12,282,9616,424035,22794444,1441538178,104721633324,...];
C=[1,1,18,585,26088,1443708,94316940,7064386296,595172880432,...];
D=[1,1,24,996,54944,3668826,283322664,24650121400,2376215009736,...];
E=[1,1,30,1515,99640,7802145,696663576,69221991825,7536986249580,...];
F=[1,1,36,2142,163632,14708421,1492326612,166960071642,...]; ...

Crossrefs

Cf. A095793, A138211, A138212, A138213, A138214, A138215.

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(6*(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)}

A302686 a(n) = [x^n] 1 + x*(1 + x*(1 + x*(1 + x*(1 + ...)^(4*n))^(3*n))^(2*n))^n.

Original entry on oeis.org

1, 1, 2, 21, 596, 32805, 2960496, 396523540, 73803150440, 18216533196693, 5757491981210470, 2267526164705341925, 1088820552191787545688, 626169526288460672060244, 424903177461959840892846066, 335946105815409394263421836000, 306145042287138023678922165314512
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 11 2018

Keywords

Crossrefs

Cf. A095793, A138212, A138213, A138214, A138215, A138216, A302657.

Programs

  • Mathematica
    Table[SeriesCoefficient[1 + x Fold[(x #1 + 1)^(n #2) &, 0, Reverse[Range[n]]], {x, 0, n}], {n, 0, 16}]

A302688 Expansion of 1 + x*(1 + 2*x*(1 + 3*x*(1 + 4*x*(1 + 5*x*(1 + ...)^5)^4)^3)^2).

Original entry on oeis.org

1, 1, 2, 12, 162, 3888, 144768, 7693920, 551981520, 51355426992, 6010929609408, 864202875949440, 149698423474606080, 30747550680449611200, 7388611598645058636000, 2053517715502048081023360, 653614372412684344833419520, 236202930442590804658824312960
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 11 2018

Keywords

Comments

(a(n) / n!^2)^(1/n) tends to 1.36594... - Vaclav Kotesovec, Apr 12 2018

Links

Crossrefs

Cf. A095793, A128318, A128319, A138211, A138212.

Programs

  • Mathematica
    nmax = 17; CoefficientList[Series[1 + x Fold[((#2 + 1) x #1 + 1)^#2 &, 0, Reverse[Range[nmax]]], {x, 0, nmax}], x]

Formula

G.f. A(x) = 1 + x + 2*x^2 + 12*x^3 + 162*x^4 + 3888*x^5 + 144768*x^6 + 7693920*x^7 + 551981520*x^8 + ...
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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