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.

A196191 G.f. satisfies A(x) = 1/Product_{n>=1} (1 - x^n/A(x^n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 3, 2, 3, 4, 4, 4, 6, 7, 7, 8, 10, 11, 12, 14, 17, 18, 20, 22, 26, 30, 31, 37, 39, 46, 49, 54, 61, 69, 74, 82, 91, 100, 114, 119, 136, 149, 159, 176, 193, 214, 227, 255, 276, 303, 324, 360, 394, 420, 462, 496, 548, 590, 638, 692, 749, 812, 874, 946, 1035, 1115, 1191, 1292, 1395, 1503
Offset: 0

Views

Author

Paul D. Hanna, Sep 28 2011

Keywords

Comments

The rate of growth of this sequence is surprisingly slow.

Examples

			G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + x^6 + 3*x^7 + 2*x^8 +...
where
A(x) = 1/((1 - x/A(x)) * (1 - x^2/A(x^2)) * (1 - x^3/A(x^3)) *...).

Links

Crossrefs

Cf. A050383, A196192.

Programs

  • PARI
    {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, (1-x^k/subst(A, x, x^k+x*O(x^n))))); polcoeff(A, n)}

A205772 G.f. satisfies: A(x) = 1/Product_{n>=1} (1 - 2*x^n*A(x^n)).

Original entry on oeis.org

1, 2, 10, 50, 290, 1766, 11442, 76522, 526574, 3697722, 26403186, 191072922, 1398344838, 10330855286, 76945148882, 577135722754, 4355579825058, 33050011129198, 251996066644866, 1929712025078322, 14834772898730766, 114445491235869774
Offset: 0

Views

Author

Paul D. Hanna, Jan 31 2012

Keywords

Examples

			G.f.: A(x) = 1 + 2*x + 10*x^2 + 50*x^3 + 290*x^4 + 1766*x^5 +...,
where A(x) = 1/((1 - 2*x*A(x)) * (1 - 2*x^2*A(x^2)) * (1 - 2*x^3*A(x^3)) * ...).

Crossrefs

Cf. A050383, A196192, A205773.

Programs

  • PARI
    {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, (1-2*x^k*subst(A, x, x^k+x*O(x^n))))); polcoeff(A, n)}

A205773 G.f. satisfies: A(x) = 1/Product_{n>=1} (1 - 3*x^n*A(x^n)).

Original entry on oeis.org

1, 3, 21, 156, 1335, 12153, 116778, 1160715, 11848530, 123420648, 1306709841, 14019657771, 152092615971, 1665531792021, 18386262679557, 204393214435791, 2286101345820933, 25708109998131381, 290490321604346535, 3296566844230833750, 37555644504960139647
Offset: 0

Views

Author

Paul D. Hanna, Jan 31 2012

Keywords

Examples

			G.f.: A(x) = 1 + 3*x + 21*x^2 + 156*x^3 + 1335*x^4 + 12153*x^5 +...
where
A(x) = 1/((1 - 3*x*A(x)) * (1 - 3*x^2*A(x^2)) * (1 - 3*x^3*A(x^3)) *...).

Crossrefs

Cf. A050383, A196192, A205772.

Programs

  • PARI
    {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, (1-3*x^k*subst(A, x, x^k+x*O(x^n))))); polcoeff(A, n)}

A205774 G.f. satisfies: A(x) = 1/Product_{n>=1} (1 - x^n*A(x^n)^3).

Original entry on oeis.org

1, 1, 5, 27, 177, 1245, 9399, 73659, 595510, 4923724, 41451675, 354071010, 3061018302, 26732084764, 235476740731, 2089770720125, 18666863392846, 167697751329817, 1514206777182411, 13734387733516323, 125083419013852945, 1143367086845429280
Offset: 0

Views

Author

Paul D. Hanna, Jan 31 2012

Keywords

Examples

			 G.f.: A(x) = 1 + x + 5*x^2 + 27*x^3 + 177*x^4 + 1245*x^5 +...
where
A(x) = 1/((1 - x*A(x)^3) * (1 - x^2*A(x^2)^3) * (1 - x^3*A(x^3)^3) *...).

Crossrefs

Cf. A050383, A196192, A205775, A196191.

A205775 G.f. satisfies: A(x) = 1/Product_{n>=1} (1 - x^n*A(x^n)^n).

Original entry on oeis.org

1, 1, 3, 8, 26, 79, 276, 936, 3376, 12259, 45648, 171739, 655664, 2524835, 9813259, 38410167, 151332137, 599541153, 2387199083, 9547195445, 38335338712, 154484001619, 624579964260, 2532713370789, 10298393401623, 41979975505800, 171522040764060
Offset: 0

Views

Author

Paul D. Hanna, Jan 31 2012

Keywords

Examples

			 G.f.: A(x) = 1 + x + 3*x^2 + 8*x^3 + 26*x^4 + 79*x^5 + 276*x^6 + 936*x^7 +...
where
A(x) = 1/((1 - x*A(x)) * (1 - x^2*A(x^2)^2) * (1 - x^3*A(x^3)^3) *...).

Crossrefs

Cf. A050383, A196192, A205774, A196191.
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.