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.

A385205 G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^4 )^(1/5).

Original entry on oeis.org

1, 5, 50, 500, 4375, 27500, 0, -3562500, -70078125, -876562500, -6926562500, 0, 1189169921875, 25690820312500, 346441406250000, 2911880859375000, 0, -550017993164062500, -12339622131347656250, -171953389892578125000, -1487552714691162109375, 0
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2025

Keywords

Crossrefs

Cf. A078534, A299958, A385203, A385204.
Cf. A182122, A376636, A385207.

Programs

  • PARI
    a(n) = 25^n*binomial(4*n/5+1/5, n)/(4*n+1);

Formula

a(n) = 25^n * binomial(4*n/5+1/5,n)/(4*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^3).
G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(4/5)) )^(1/4).
a(5*n+1) = 0 for n > 0.
G.f.: 1/B(x), where B(x) is the g.f. of A299958.

A385206 G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x) )^(1/7).

Original entry on oeis.org

1, 7, -98, 1715, -28812, 369754, 0, -234003861, 11187831655, -379208609780, 10505577339166, -237021026782414, 3747904201751920, 0, -3136632447485449416, 165539296779239527515, -6087083256734433868530, 180571542422445599417377, -4318405727843353425012650
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2025

Keywords

Links

Crossrefs

Cf. A385207, A385208.
Cf. A182122.

Programs

  • PARI
    a(n) = 49^n*binomial(n/7+1/7, n)/(n+1);
  • PARI
    my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+49*x)^(1/7))/x)

Formula

a(n) = 49^n * binomial(n/7+1/7,n)/(n+1).
G.f. A(x) satisfies A(x) = 1/A(-x/A(x)^5).
G.f.: (1/x) * Series_Reversion(x/(1+49*x)^(1/7)).
a(7*n+6) = 0 for n >= 0.

A385208 G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x)^8 )^(1/7).

Original entry on oeis.org

1, 7, 245, 11319, 593047, 33429123, 1977326743, 121034349975, 7601257418678, 487008549508481, 31705597390195820, 2091361378163375955, 139468121325692304390, 9387480337647754305649, 636914947847207765431080, 43512658997082838985965655, 2990750175103769856729417627
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2025

Keywords

Crossrefs

Cf. A078531, A078532, A078533, A078534, A078535.
Cf. A385206, A385207.

Programs

  • PARI
    a(n) = 49^n*binomial(8*n/7+1/7, n)/(8*n+1);

Formula

a(n) = 49^n * binomial(8*n/7+1/7,n)/(8*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^9).
G.f.: ( (1/x) * Series_Reversion(x/(1+49*x)^(8/7)) )^(1/8).
Showing 1-3 of 3 results.

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

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