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.

Previous Showing 11-14 of 14 results.

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).

A049394 Expansion of (1-25*x)^(-6/5).

Original entry on oeis.org

1, 30, 825, 22000, 577500, 15015000, 387887500, 9974250000, 255590156250, 6531748437500, 166559585156250, 4239698531250000, 107759004335937500, 2735420879296875000, 69362458010742187500, 1757182269605468750000
Offset: 0

Views

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

Examples

			(1-x)^(-6/5) = 1 + 6/5*x + 33/25*x^2 + 176/125*x^3 + ...

Crossrefs

Cf. A034688.

Programs

  • Mathematica
    CoefficientList[Series[(1-25*x)^(-6/5), {x, 0, 15}], x] (* Georg Fischer, Jan 16 2020 *)

Formula

G.f.: (1-25*x)^(-6/5).
a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k+6).
a(n) ~ 5*Gamma(1/5)^-1*n^(1/5)*5^(2*n)*{1 + 3/25*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

Extensions

Definition corrected by Georg Fischer, Jan 16 2020

A049390 Expansion of (1-25*x)^(4/5).

Original entry on oeis.org

1, -20, -50, -500, -6875, -110000, -1925000, -35750000, -692656250, -13853125000, -283989062500, -5937953125000, -126181503906250, -2717755468750000, -59208244140625000, -1302581371093750000
Offset: 0

Views

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

Examples

			(1-x)^(4/5) = 1 - 4/5*x - 2/25*x^2 - 4/125*x^3 - ...

Crossrefs

Cf. A034688.

Programs

  • Mathematica
    CoefficientList[Series[(1-25x)^(4/5),{x,0,20}],x] (* Harvey P. Dale, Dec 14 2017 *)

Formula

G.f.: (1-25*x)^(4/5).
a(n) = 5^n/n! * product[ k=0..n-1 ] (5*k-4).
a(n) ~ -4/5*Gamma(1/5)^-1*n^(-9/5)*5^(2*n)*{1 + 18/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

Extensions

Definition adjusted by Harvey P. Dale, Dec 14 2017.
Previous Showing 11-14 of 14 results.

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