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.

A145158 G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x).

Original entry on oeis.org

1, 1, 3, 16, 121, 1143, 12570, 154551, 2072547, 29829412, 455731327, 7332989616, 123548350018, 2169987439342, 39595583375433, 748541216196285, 14628467191450947, 294984129900772611, 6128372452917891216
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 121*x^4 + 1143*x^5 +...
x/A(x)^2 = x - 2*x^2 - 3*x^3 - 18*x^4 - 150*x^5 - 1518*x^6 -...
1/A(x) = 1 - x - 2*x^2 - 11*x^3 - 88*x^4 - 869*x^5 - 9876*x^6 -...
Series_Reversion[x/A(x)^2] = x + 2*x^2 + 11*x^3 + 88*x^4 + 869*x^5 +...
		

Crossrefs

Programs

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

Formula

G.f. satisfies: 1 - 1/A(x) = x*A( 1 - 1/A(x) )^2.
Self-convolution yields A145159.

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.

A145166 G.f. A(x) satisfies A(x/A(x)) = 1/(1-x)^5.

Original entry on oeis.org

1, 5, 40, 510, 9095, 203376, 5323465, 156499485, 5035901400, 174413579095, 6427089519606, 249922852038280, 10193367893772075, 434056833951578950, 19227980415244742745, 883565304511733011301, 42019895809388715550450
Offset: 0

Views

Author

Paul D. Hanna, Oct 03 2008

Keywords

Crossrefs

Cf. A145165.

Programs

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

Formula

Self-convolution 5th power of A145165.
Showing 1-5 of 5 results.