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 1-7 of 7 results.

A138212 G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(2n))...)^6)^4)^2.

Original entry on oeis.org

1, 1, 2, 9, 68, 732, 10250, 176654, 3613044, 85476720, 2295275372, 68949496421, 2290588299708, 83374406924240, 3299390271801838, 141034101443780374, 6475752407825487220, 317866884692663325892, 16609896989101220207880
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=[1,1,2,9,68,732,10250,176654,3613044,85476720,...];
B=[1,1,4,30,328,4677,81888,1696086,40520620,1096342026,...];
C=[1,1,6,63,908,16311,347466,8519957,235763712,7259384208,...];
D=[1,1,8,108,1936,42110,1062416,30283824,958845640,...];
E=[1,1,10,165,3540,90550,2646522,86251140,3086189660,...];
F=[1,1,12,234,5848,172107,5725392,210342902,8410505748,...]; ...

Links

Crossrefs

Cf. A095793, A138211, 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))); 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)}

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)}

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 1-7 of 7 results.

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