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 1-3 of 3 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.

A145169 G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x)^3.

Original entry on oeis.org

1, 3, 24, 361, 7851, 214245, 6815986, 242659191, 9431036685, 393771017068, 17469277612998, 817033067908275, 40050828368606412, 2048642917085523633, 108968676087557745858, 6010617981960195923285, 343038687551360605111371
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Cf. A145167, A145168, A145170 (A^2).

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n),B);for(n=0,n,B=serreverse(x/A^2);A=1/(1-B)^3);polcoeff(A,n)}

Formula

Self-convolution cube of A145167.
Self-convolution square yields A145170.

A145168 G.f. A(x) satisfies A(x/A(x)^3) = 1/(1-x)^2.

Original entry on oeis.org

1, 2, 15, 226, 4959, 136338, 4361818, 155947386, 6080986701, 254568183028, 11318103523886, 530301559146450, 26035289254487166, 1333502730683975402, 71012366873757289557, 3921010145962481940986, 223985973308662486807733
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Cf. A145167, A145169, A145170 (A^3).

Programs

  • PARI
    {a(n)=local(A=1+x+x*O(x^n),B);for(n=0,n,B=serreverse(x/A^3);A=1/(1-B)^2);polcoeff(A,n)}

Formula

Self-convolution square of A145167.
Self-convolution cube yields A145170.
Showing 1-3 of 3 results.