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.

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A385471 Expansion of e.g.f. 1/(1 - 3 * arctanh(x)).

Original entry on oeis.org

1, 3, 18, 168, 2088, 32472, 605952, 13192848, 328268160, 9189103104, 285808290048, 9778434400512, 364965976571904, 14756982055363584, 642580290860378112, 29979230177385750528, 1491908801018949697536, 78884742832151951278080, 4416389166601900315901952
Offset: 0

Views

Author

Seiichi Manyama, Jun 30 2025

Keywords

Crossrefs

Cf. A296676, A385470.
Cf. A111594, A385469.

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A385469.
E.g.f.: 1/(1 - (3/2) * log((1+x)/(1-x))).
a(n) = Sum_{k=0..n} 3^k * k! * A111594(n,k).

A385472 Expansion of e.g.f. 1/(1 - arctanh(2*x))^(1/2).

Original entry on oeis.org

1, 1, 3, 23, 201, 2529, 36027, 633975, 12445521, 282376065, 7045758003, 196111046295, 5929900611225, 195773173735905, 6950809317622635, 265652001656970615, 10828342476187312545, 470368564694268015105, 21643209863062015977315, 1053344875062427351601175
Offset: 0

Views

Author

Seiichi Manyama, Jun 30 2025

Keywords

Crossrefs

Cf. A296676, A385473.
Cf. A001147, A111594.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-atanh(2*x))^(1/2)))

Formula

E.g.f.: 1/(1 - (1/2) * log((1+2*x)/(1-2*x)))^(1/2).
a(n) = Sum_{k=0..n} A001147(k) * 2^(n-k) * A111594(n,k).

A385473 Expansion of e.g.f. 1/(1 - arctanh(3*x))^(1/3).

Original entry on oeis.org

1, 1, 4, 46, 568, 10624, 218656, 5702752, 163568128, 5497133824, 201702168064, 8319367856128, 371416377318400, 18185429803469824, 955872746109276160, 54228988018125125632, 3278679608280623841280, 211600457615794941460480, 14461966051190623712051200
Offset: 0

Views

Author

Seiichi Manyama, Jun 30 2025

Keywords

Crossrefs

Cf. A296676, A385472.
Cf. A007559, A111594.

Programs

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

Formula

E.g.f.: 1/(1 - (1/2) * log((1+3*x)/(1-3*x)))^(1/3).
a(n) = Sum_{k=0..n} A007559(k) * 3^(n-k) * A111594(n,k).
Previous Showing 11-13 of 13 results.

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

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