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.

A370780 Expansion of ( (1 + x)*(1 - 17*x)*(1 + 289*x) )^(1/3).

Original entry on oeis.org

1, 91, -9828, 1535868, -294731892, 62322050700, -13990450587012, 3270320252339868, -787131217405990548, 193694053976566000812, -48497295306135216560292, 12313491783703337923916220, -3162498663877264843739477172
Offset: 0

Views

Author

Seiichi Manyama, Mar 01 2024

Keywords

Comments

The cube root of F(x) = (1 + x)*(1 - (3*k+2)*x)*(1 + (3*k+2)^2*x) is an integer series because F(x) == (1+x)*(1 + 2*x - 8*x^2) == (1+x)^3 (mod 9).

Crossrefs

Cf. A370145, A370149, A370779.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(((1+x)*(1-17*x)*(1+289*x))^(1/3))

A370782 Expansion of 1 / ( (1 - x)*(1 + 5*x)*(1 - 25*x) )^(1/3).

Original entry on oeis.org

1, 7, 133, 2539, 53305, 1155679, 25714333, 582045667, 13346038321, 309067047415, 7213999049845, 169466050348315, 4002188759121385, 94941811661199055, 2260887088517478925, 54017663776267303315, 1294331605116743179105, 31092684363296020670695
Offset: 0

Views

Author

Seiichi Manyama, Mar 01 2024

Keywords

Crossrefs

Cf. A370779.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1+5*x)*(1-25*x))^(1/3))

Formula

a(n) ~ 5^(2*n+1) / (Gamma(1/3) * 2^(4/3) * 3^(2/3) * n^(2/3)). - Vaclav Kotesovec, Mar 10 2024
Showing 1-2 of 2 results.

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

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