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 1-6 of 6 results.

A385203 G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^2 )^(1/5).

Original entry on oeis.org

1, 5, 0, -125, 625, 5625, -87500, 0, 9140625, -60156250, -653125000, 11654296875, 0, -1470068359375, 10353515625000, 118916992187500, -2225148925781250, 0, 302784667968750000, -2199076690673828125, -25952287445068359375, 497460246276855468750, 0
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2025

Keywords

Crossrefs

Cf. A078534, A385204, A385205.

Programs

  • PARI
    a(n) = 25^n*binomial(2*n/5+1/5, n)/(2*n+1);

Formula

a(n) = 25^n * binomial(2*n/5+1/5,n)/(2*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x/A(x)).
G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(2/5)) )^(1/2).
a(5*n+2) = 0 for n >= 0.

A385204 G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^3 )^(1/5).

Original entry on oeis.org

1, 5, 25, 0, -1250, -6875, 65625, 1062500, 0, -116796875, -782031250, 8609375000, 155390625000, 0, -19950927734375, -141498046875000, 1635108642578125, 30759411621093750, 0, -4223049316406250000, -30787073669433593750, 364567847442626953125
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2025

Keywords

Crossrefs

Cf. A078534, A385203, A385205.

Programs

  • PARI
    a(n) = 25^n*binomial(3*n/5+1/5, n)/(3*n+1);

Formula

a(n) = 25^n * binomial(3*n/5+1/5,n)/(3*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x*A(x)).
G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(3/5)) )^(1/3).
a(5*n+3) = 0 for n >= 0.
G.f.: 1/B(-x), where B(x) is the g.f. of A385203.

A385207 G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x)^6 )^(1/7).

Original entry on oeis.org

1, 7, 147, 3430, 79233, 1714314, 32471124, 450360372, 0, -313409171166, -15459345780879, -537166232508360, -15185812043764453, -348420909370148580, -5588125164812112720, 0, 4783756561471246040577, 254794190560328322173970, 9445124186699596552669050
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2025

Keywords

Crossrefs

Cf. A385206, A385208.
Cf. A182122, A376636, A385205.

Programs

  • PARI
    a(n) = 49^n*binomial(6*n/7+1/7, n)/(6*n+1);

Formula

a(n) = 49^n * binomial(6*n/7+1/7,n)/(6*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)^(6/7)) )^(1/6).
a(7*n+1) = 0 for n > 0.
G.f.: 1/B(-x), where B(x) is the g.f. of A385206.

A380465 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^2 )^(1/5).

Original entry on oeis.org

1, 5, 125, 4250, 166250, 7052500, 315459375, 14648437500, 699404062500, 34120414453125, 1693355782421875, 85222795492187500, 4339218139648437500, 223115431527734375000, 11568972340119140625000, 604249120575386718750000, 31761084429202554931640625, 1678825356066226959228515625
Offset: 0

Views

Author

Seiichi Manyama, Jun 23 2025

Keywords

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380466, A380471.

Programs

  • PARI
    a(n) = 25^n*binomial(7*n/5+1/5, n)/(7*n+1);

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^7 )^(1/5).
a(n) = 25^n * binomial(7*n/5+1/5,n)/(7*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^9).
G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(7/5)) )^(1/7).

A380466 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^3 )^(1/5).

Original entry on oeis.org

1, 5, 150, 6250, 301875, 15868125, 881237500, 50865750000, 3021240234375, 183454158593750, 11336659803906250, 710625236343750000, 45075347315400390625, 2887845039367675781250, 186601230428607421875000, 12146710229056792968750000, 795792421294273872070312500
Offset: 0

Views

Author

Seiichi Manyama, Jun 23 2025

Keywords

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380465, A380471.

Programs

  • PARI
    a(n) = 25^n*binomial(8*n/5+1/5, n)/(8*n+1);

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^8 )^(1/5).
a(n) = 25^n * binomial(8*n/5+1/5,n)/(8*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^11).
G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(8/5)) )^(1/8).

A380471 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^4 )^(1/5).

Original entry on oeis.org

1, 5, 175, 8625, 495000, 30980625, 2050781250, 141187921875, 10006590468750, 725240531640625, 53503504196484375, 4004478454589843750, 303320955472031250000, 23207794539155419921875, 1791025435519151367187500, 139250846557940616210937500, 10897102765738964080810546875
Offset: 0

Views

Author

Seiichi Manyama, Jun 23 2025

Keywords

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380465, A380466.

Programs

  • PARI
    a(n) = 25^n*binomial(9*n/5+1/5, n)/(9*n+1);

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^9 )^(1/5).
a(n) = 25^n * binomial(9*n/5+1/5,n)/(9*n+1).
G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^13).
G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(9/5)) )^(1/9).
Showing 1-6 of 6 results.

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