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 1-4 of 4 results.

A365982 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+3) / (5*k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 0, 80, 0, 5040, 13440, 0, 3326400, 5913600, 479001600, 3632428800, 5381376000, 1399882176000, 6586804224000, 364469833728000, 5019809832576000, 18772392038400000, 2898136435138560000, 24517466017228800000, 1203790902897623040000
Offset: 0

Views

Author

Seiichi Manyama, Sep 24 2023

Keywords

Crossrefs

Cf. A355284, A365980, A365981.
Cf. A365912, A365974.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+3)/(5*k+3)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/5)} (5*k+2)! * binomial(n,5*k+3) * a(n-5*k-3).

A365981 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+3) / (4*k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 0, 80, 720, 0, 13440, 345600, 3628800, 5913600, 296524800, 7062681600, 92559667200, 442810368000, 18037334016000, 459627769036800, 7475081822208000, 65867064606720000, 2634706112643072000, 74102151110787072000, 1464478283948359680000
Offset: 0

Views

Author

Seiichi Manyama, Sep 24 2023

Keywords

Crossrefs

Cf. A355284, A365980, A365982.
Cf. A365911.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+3)/(4*k+3)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/4)} (4*k+2)! * binomial(n,4*k+3) * a(n-4*k-3).

A365980 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(2*k+3) / (2*k+3) ).

Original entry on oeis.org

1, 0, 0, 2, 0, 24, 80, 720, 5376, 53760, 490752, 6289920, 68766720, 1024607232, 13520332800, 226177695744, 3498759290880, 65257155624960, 1153246338220032, 23793010526453760, 472374431008948224, 10686755493583257600, 235406405307208826880
Offset: 0

Views

Author

Seiichi Manyama, Sep 23 2023

Keywords

Crossrefs

Cf. A355284, A365981, A365982.
Cf. A130915, A296676.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-atanh(x))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/2)} (2*k+2)! * binomial(n,2*k+3) * a(n-2*k-3).
E.g.f.: 1 / ( 1 + x - arctanh(x) ).

A355285 Expansion of e.g.f. 1 / (1 + x + x^2/2 + x^3/3 + log(1 - x)).

Original entry on oeis.org

1, 0, 0, 0, 6, 24, 120, 720, 7560, 76608, 810432, 9141120, 118015920, 1666336320, 25211774016, 404932155264, 6951992261760, 127203705538560, 2467434718218240, 50477473338494976, 1086707769452699904, 24573149993692615680, 582367494447600583680, 14430857455114783119360
Offset: 0

Views

Author

Ilya Gutkovskiy, Jun 26 2022

Keywords

Crossrefs

Cf. A007840, A047865, A226226, A232475, A355284.

Programs

  • Mathematica
    nmax = 23; CoefficientList[Series[1/(1 + x + x^2/2 + x^3/3 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 4, n}]; Table[a[n], {n, 0, 23}]
  • PARI
    my(x='x+O('x^30)); Vec(serlaplace(1/(1 + x + x^2/2 + x^3/3 + log(1 - x)))) \\ Michel Marcus, Jun 27 2022

Formula

E.g.f.: 1 / (1 - Sum_{k>=4} x^k/k).
a(0) = 1; a(n) = Sum_{k=4..n} binomial(n,k) * (k-1)! * a(n-k).
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.