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 1-3 of 3 results.

A376475 E.g.f. satisfies A(x) = exp( x^3*A(x)^3 / (1 - x*A(x)) ).

Original entry on oeis.org

1, 0, 0, 6, 24, 120, 3240, 45360, 584640, 13668480, 322963200, 7224940800, 201040963200, 6254004556800, 197219089267200, 6845849673062400, 260976932536320000, 10410615332941824000, 441056225586706329600, 20015606466369626112000, 955852013167308601344000, 47944066629381635801088000
Offset: 0

Views

Author

Seiichi Manyama, Sep 24 2024

Keywords

Links

Crossrefs

Cf. A052873, A376474.
Cf. A293049.

Programs

  • PARI
    a(n) = n!*sum(k=0, n\3, (n+1)^(k-1)*binomial(n-2*k-1, n-3*k)/k!);

Formula

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

A376494 E.g.f. satisfies A(x) = exp(x^2 * A(x)^2 / (1 - x)).

Original entry on oeis.org

1, 0, 2, 6, 84, 720, 12000, 178920, 3744720, 79531200, 2056652640, 56284351200, 1753673423040, 58443081016320, 2142625074670080, 83948606126985600, 3549356731374854400, 159643527455123712000, 7656564912324122995200
Offset: 0

Views

Author

Seiichi Manyama, Sep 25 2024

Keywords

Links

Crossrefs

Cf. A052868, A376495.
Cf. A052845, A376474.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x^2/(1-x))/2)))
  • PARI
    a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(n-k-1, n-2*k)/k!);

Formula

E.g.f.: exp( -LambertW(-2*x^2 / (1-x))/2 ).
a(n) = n! * Sum_{k=0..floor(n/2)} (2*k+1)^(k-1) * binomial(n-k-1,n-2*k)/k!.
a(n) ~ sqrt(16 + 2*exp(-1) - 2*exp(-1/2)*sqrt(exp(-1)+8)) * (exp(1/2)*sqrt(exp(-1)+8) - 1) * 2^(2*n-2) * n^(n-1) / ((4 + exp(-1) - exp(-1/2)*sqrt(exp(-1)+8)) * (sqrt(1 + 8*exp(1)) - 1)^n). - Vaclav Kotesovec, Aug 05 2025

A376558 E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x^2*A(x)^2) ).

Original entry on oeis.org

1, 1, 3, 22, 245, 3576, 65527, 1449904, 37596393, 1118442880, 37559084651, 1405597826304, 58012540741597, 2617923512200192, 128240561732097375, 6777245042104293376, 384358793388984148433, 23284761629109883600896, 1500714780345430134323923
Offset: 0

Views

Author

Seiichi Manyama, Sep 28 2024

Keywords

Links

Crossrefs

Cf. A052873, A376563.
Cf. A088009, A376474.

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*binomial(n-k-1, k)/(n-2*k)!);

Formula

E.g.f.: (1/x) * Series_Reversion( x*exp(-x / (1 - x^2)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-2*k-1) * binomial(n-k-1,k)/(n-2*k)!.
Showing 1-3 of 3 results.

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

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