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.

A365085 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^2.

Original entry on oeis.org

1, 1, -1, -2, 5, 6, -30, -13, 189, -56, -1188, 1266, 7194, -14377, -40183, 135278, 188773, -1151800, -503880, 9109076, -3419924, -67220176, 80390824, 458183898, -998680470, -2794491329, 10156144385, 13919066170, -92250872385, -36047778330, 769826420850, -339940775445
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2023

Keywords

Crossrefs

Cf. A090192, A365086, A365087, A365088.
Cf. A106510, A364735.

Programs

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

Formula

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

A365086 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^3.

Original entry on oeis.org

1, 1, -2, -2, 15, -4, -122, 204, 903, -3374, -4635, 43539, -13233, -475123, 873392, 4244591, -16906773, -24952174, 244162840, -74520792, -2901715074, 5483226036, 27740164293, -112969486284, -172903931727, 1714556657881, -513739179725, -21235809823325
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2023

Keywords

Crossrefs

Cf. A090192, A365085, A365087, A365088.
Cf. A127896, A161797, A364736.

Programs

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

Formula

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

A365088 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^5.

Original entry on oeis.org

1, 1, -4, 1, 46, -129, -405, 3319, -1617, -59258, 199541, 642170, -6038395, 3886091, 119884973, -440626784, -1367688245, 14055527190, -11043763380, -290488387366, 1137260033731, 3336325340735, -36966844508130, 34098313310315, 776097820004580
Offset: 0

Views

Author

Seiichi Manyama, Aug 21 2023

Keywords

Crossrefs

Cf. A090192, A365085, A365086, A365087.
Cf. A321799, A364738, A365084.

Programs

  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+4*k-1, n-k)/(n-k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n+4*k-1,n-k) / (n-k+1).

A365111 G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^4.

Original entry on oeis.org

1, 1, -4, 6, 16, -119, 240, 630, -5656, 13044, 31568, -323102, 816172, 1772553, -20373748, 55339784, 105991968, -1366239119, 3950894080, 6570520544, -95534073488, 292319792622, 414994066768, -6884779019086, 22198354364212, 26341578132594, -507524582140912
Offset: 0

Views

Author

Seiichi Manyama, Aug 22 2023

Keywords

Crossrefs

Cf. A007440, A365109, A365110, A365112.
Cf. A365087.

Programs

  • PARI
    a(n, s=4) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

Formula

If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
Showing 1-4 of 4 results.

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

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