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 1-5 of 5 results.

A145167 G.f. A(x) satisfies A(x/A(x)^6) = 1/(1-x).

Original entry on oeis.org

1, 1, 7, 106, 2349, 65078, 2093770, 75175383, 2941004409, 123442051582, 5500018250128, 258162075155942, 12693904947530988, 651028563908092621, 34708995997762871047, 1918449419812267920842, 109690826250327197055475
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Programs

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

Formula

G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^6.
Self-convolution square yields A145168.
Self-convolution cube yields A145169.
Self-convolution 6th power yields A145170.

A145160 G.f. A(x) satisfies A(x/A(x)^3) = 1/(1-x).

Original entry on oeis.org

1, 1, 4, 31, 347, 4860, 79174, 1440837, 28584939, 608533714, 13751688892, 327333165775, 8160149459870, 212121519165566, 5730205766494409, 160425928432680795, 4644491031188023566, 138792548776938444503
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n));for(n=0,n,B=serreverse(x/A^3);A=1/(1-B));polcoeff(A,n)}

Formula

G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^3.
Self-convolution cube yields A145161.

A145162 G.f. A(x) satisfies A(x/A(x)^4) = 1/(1-x).

Original entry on oeis.org

1, 1, 5, 51, 757, 14058, 303443, 7313188, 192096189, 5413972155, 161972306602, 5104569475976, 168500227127871, 5800706769824992, 207552636468976072, 7697809237540240440, 295284422299359774761, 11693774821978063710405
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Programs

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

Formula

G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^4.
Self-convolution square yields A145163.
Self-convolution 4th power yields A145164.

A145165 G.f. A(x) satisfies A(x/A(x)^5) = 1/(1-x).

Original entry on oeis.org

1, 1, 6, 76, 1406, 32531, 874407, 26234503, 857727024, 30087607090, 1120358453641, 43948073274103, 1805827523343241, 77390779901965470, 3447553371343457810, 159209478315871014816, 7605143367385966288569
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Programs

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

Formula

G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^5.
Self-convolution 5th power yields A145166.

A145159 G.f. A(x) satisfies A(x/A(x)) = 1/(1-x)^2.

Original entry on oeis.org

1, 2, 7, 38, 283, 2624, 28408, 344972, 4580833, 65410070, 992850781, 15888876224, 266464473274, 4661494891166, 84761554257517, 1597453996121132, 31132664696108551, 626239933178389916, 12981131500452667888
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Cf. A145158.

Programs

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

Formula

Self-convolution of A145158.
Showing 1-5 of 5 results.