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.

A365177 E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)^3).

Original entry on oeis.org

1, 1, 10, 201, 6220, 261465, 13925286, 898994383, 68240292856, 5956670911041, 587896878021130, 64738492669538391, 7869297152389747284, 1046629627952327990545, 151192146681811716344878, 23573456446401808474471455, 3945806733850334447131941616
Offset: 0

Views

Author

Seiichi Manyama, Aug 25 2023

Keywords

Crossrefs

Cf. A364987, A364989, A365175, A365176.

Programs

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

Formula

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

A365175 E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)).

Original entry on oeis.org

1, 1, 10, 189, 5476, 215145, 10701006, 644909503, 45687408712, 3721382812305, 342689189598010, 35206864089944151, 3992473080042706524, 495361299387667990537, 66752437447119717428422, 9708649781691227748131535, 1515863453268825963300368656
Offset: 0

Views

Author

Seiichi Manyama, Aug 25 2023

Keywords

Crossrefs

Cf. A364987, A364989, A365176, A365177.
Cf. A161633, A213644, A364984.

Programs

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

Formula

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

A377549 E.g.f. satisfies A(x) = 1 + x*A(x)^5*exp(x*A(x)^2).

Original entry on oeis.org

1, 1, 12, 285, 10444, 520465, 32882406, 2519264797, 227003238792, 23526134771553, 2757165645132010, 360564513170510341, 52053350012338720332, 8222888925567102799441, 1410913077291231960911934, 261306906300110395598900685, 51955790654759866661097707536
Offset: 0

Views

Author

Seiichi Manyama, Oct 31 2024

Keywords

Crossrefs

Cf. A364980, A364982, A364985, A365176.
Cf. A377547.

Programs

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

Formula

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