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.

A364736 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^3).

Original entry on oeis.org

1, 1, 0, -3, -3, 17, 45, -90, -546, 130, 5832, 7074, -53625, -159214, 374517, 2419131, -728364, -30011530, -37519884, 307731042, 940757526, -2343385995, -15421126275, 5164279686, 203045257272, 255851517115, -2186669342070, -6760669947375, 17391580425180
Offset: 0

Views

Author

Seiichi Manyama, Aug 05 2023

Keywords

Crossrefs

Cf. A364735, A364737, A364738.
Cf. A300048.

Programs

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

Formula

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

A364738 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^5).

Original entry on oeis.org

1, 1, 0, -5, -10, 40, 245, -26, -4375, -11410, 53040, 377850, -12320, -7988194, -23011625, 106662595, 824671575, 64095550, -18490968680, -57052839001, 254513058375, 2098532784575, 419490572800, -48205987947600, -157458581103395, 666628546612606, 5824573247731250
Offset: 0

Views

Author

Seiichi Manyama, Aug 05 2023

Keywords

Crossrefs

Cf. A364735, A364736, A364737.
Cf. A364734.

Programs

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

Formula

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

A364737 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x)^4).

Original entry on oeis.org

1, 1, 0, -4, -6, 28, 119, -116, -1820, -2128, 22212, 79877, -172700, -1652728, -857428, 25387284, 71506309, -268817888, -1838702048, 449975584, 33164610276, 68575577309, -429542625096, -2221814345660, 2539462697398, 46048818685880, 61721413191310
Offset: 0

Views

Author

Seiichi Manyama, Aug 05 2023

Keywords

Crossrefs

Cf. A364735, A364736, A364738.

Programs

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

Formula

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

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).
Showing 1-4 of 4 results.

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

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