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 1-2 of 2 results.

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).

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 1-2 of 2 results.

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

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