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.

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A060910 E.g.f.: exp(x*exp(x*exp(x)) + 1/2*x^2*exp(x*exp(x))^2 + 1/4*x^4*exp(x*exp(x))^4).

Original entry on oeis.org

1, 1, 4, 25, 200, 1941, 22552, 304207, 4660224, 79627609, 1496962736, 30645682299, 677868344056, 16102526543533, 408764126148120, 11042583947604871, 316299747976627808, 9574687031473970673
Offset: 0

Views

Author

Vladeta Jovovic, Apr 07 2001

Keywords

References

  • I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Crossrefs

Formula

E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 2, m = 4.

A060911 E.g.f.: exp(x*exp(x*exp(x*exp(x))) + 1/2*x^2*exp(x*exp(x*exp(x)))^2).

Original entry on oeis.org

1, 1, 4, 25, 218, 2331, 29152, 417607, 6746700, 121312441, 2401341056, 51857779689, 1212621122176, 30509979042115, 821524617293304, 23563369209520711, 717014609781379568, 23064363484845390513
Offset: 0

Views

Author

Vladeta Jovovic, Apr 07 2001

Keywords

References

  • I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Crossrefs

Formula

E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 3, m = 2.

A060912 E.g.f.: exp(x*exp(x*exp(x*exp(x*exp(x)))) + 1/2*x^2*exp(x*exp(x*exp(x*exp(x))))^2).

Original entry on oeis.org

1, 1, 4, 25, 218, 2451, 33112, 516727, 9117180, 179330905, 3890434256, 92271385449, 2374775505016, 65900749176835, 1961009596461840, 62275489622799751, 2101798757669917328, 75111617959762807473
Offset: 0

Views

Author

Vladeta Jovovic, Apr 07 2001

Keywords

References

  • I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

Crossrefs

Formula

E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 4, m = 2.

A235325 Number of ordered pairs of endofunctions f,g on a set of n elements satisfying f(f(x)) = g(g(g(x))).

Original entry on oeis.org

1, 1, 4, 51, 1072, 31845, 1292616, 68464207, 4555593904, 369790197705
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Extensions

a(6)-a(7) from Giovanni Resta, Mar 26 2014
a(8)-a(9) from Giovanni Resta, Mar 28 2014

A235326 Number of ordered pairs of endofunctions f,g on a set of n elements satisfying f(f(f(x))) = g(g(g(x))).

Original entry on oeis.org

1, 1, 4, 51, 1504, 66525, 4196856, 359031967, 39705044464, 5476674540825
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Extensions

a(6)-a(7) from Giovanni Resta, Mar 26 2014
a(8)-a(9) from Giovanni Resta, Mar 28 2014

A235327 Number of ordered pairs of endofunctions f, g on a set of n elements satisfying f(f(x)) = g(g(x)).

Original entry on oeis.org

1, 1, 6, 69, 1144, 25045, 708336, 24564211, 1020980640, 49909891257
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Extensions

a(6)-a(7) from Giovanni Resta, Mar 26 2014
a(8)-a(9) from Giovanni Resta, Mar 28 2014

A239753 Number of pairs of functions (f,g) on a set of n elements into itself satisfying f(x) = g(f(g(x))).

Original entry on oeis.org

1, 1, 8, 87, 1312, 24685, 564336, 15168811
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Formula

a(n) <= n^2n. - Charles R Greathouse IV, Mar 26 2014

Extensions

a(6)-a(7) from Giovanni Resta, Mar 28 2014

A239754 Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(g(f(x))) = g(g(g(x))).

Original entry on oeis.org

1, 1, 8, 111, 2896, 119985, 7180776, 581563129
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Extensions

a(6)-a(7) from Giovanni Resta, Mar 28 2014

A239755 Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(g(x)) = g(f(f(x))).

Original entry on oeis.org

1, 1, 8, 123, 2776, 86265, 3498336, 179365669
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Extensions

a(6)-a(7) from Giovanni Resta, Mar 28 2014

A239756 Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(f(g(x))) = g(g(x)).

Original entry on oeis.org

1, 1, 8, 129, 3616, 151845, 8864496, 682005919
Offset: 0

Views

Author

Chad Brewbaker, Mar 26 2014

Keywords

Crossrefs

Extensions

a(6)-a(7) from Giovanni Resta, Mar 28 2014
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