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 1-5 of 5 results.

A365731 G.f. satisfies A(x) = 1 + x^4*A(x)^5*(1 + x*A(x)).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 0, 5, 11, 6, 0, 35, 120, 136, 51, 285, 1330, 2310, 1771, 3036, 14950, 35100, 40950, 47502, 175392, 503440, 791120, 927520, 2272424, 7037184, 13803405, 18643560, 33997080, 98920536, 226318196, 359255325, 578590155, 1445166360, 3584815443, 6573439928
Offset: 0

Views

Author

Seiichi Manyama, Sep 17 2023

Keywords

Links

Crossrefs

Cf. A365727, A365728, A365729, A365730.
Cf. A001002, A217358, A365725.
Cf. A215342.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(n+k+1,k) / (n+k+1).
G.f.: (1/x) * Series_Reversion( x*(1 - x^4*(1 + x)) ). - Seiichi Manyama, Sep 24 2024

A365724 G.f. satisfies A(x) = 1 + x^3*A(x)^3*(1 + x*A(x)).

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 3, 7, 4, 12, 45, 55, 77, 286, 546, 728, 1960, 4760, 7548, 15504, 39729, 75582, 140448, 336490, 723327, 1366200, 2992990, 6758895, 13522275, 28094040, 63183315, 133231800, 273896532, 600805296, 1305229332, 2720740792, 5843241088, 12797739672
Offset: 0

Views

Author

Seiichi Manyama, Sep 17 2023

Keywords

Crossrefs

Cf. A308616, A365723, A365725, A365726.
Cf. A001005, A001006, A365730.
Cf. A114997.

Programs

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

Formula

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

A365727 G.f. satisfies A(x) = 1 + x^4*A(x)*(1 + x*A(x)).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 0, 1, 3, 2, 0, 1, 6, 10, 5, 1, 10, 30, 35, 15, 15, 70, 140, 127, 63, 140, 420, 631, 490, 384, 1050, 2311, 2808, 2136, 2739, 6931, 12057, 12672, 11055, 19449, 42097, 61050, 60060, 66353, 131054, 241670, 306735, 308881, 428792, 835614, 1337765
Offset: 0

Views

Author

Seiichi Manyama, Sep 17 2023

Keywords

Crossrefs

Cf. A365728, A365729, A365730, A365731.
Cf. A023427.

Programs

  • PARI
    a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(n-3*k+1, k)/(n-3*k+1));

Formula

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

A365728 G.f. satisfies A(x) = 1 + x^4*A(x)^2*(1 + x*A(x)).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 0, 2, 5, 3, 0, 5, 21, 28, 12, 14, 84, 180, 165, 97, 330, 990, 1430, 1133, 1560, 5005, 10010, 11349, 11193, 25452, 61880, 94250, 100844, 150144, 360468, 683162, 889542, 1100784, 2144397, 4536839, 7158326, 9102786, 14132580, 29078645
Offset: 0

Views

Author

Seiichi Manyama, Sep 17 2023

Keywords

Crossrefs

Cf. A365727, A365729, A365730, A365731.
Cf. A365696.

Programs

  • PARI
    a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(n-2*k+1, k)/(n-2*k+1));

Formula

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

A365729 G.f. satisfies A(x) = 1 + x^4*A(x)^3*(1 + x*A(x)).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 0, 3, 7, 4, 0, 12, 45, 55, 22, 55, 286, 546, 455, 413, 1820, 4760, 6120, 5304, 12597, 38760, 67830, 73587, 108262, 309925, 672980, 928763, 1171390, 2598310, 6270030, 10607025, 14033565, 24293880, 57256875, 112293597, 167416275, 255805056
Offset: 0

Views

Author

Seiichi Manyama, Sep 17 2023

Keywords

Crossrefs

Cf. A365727, A365728, A365730, A365731.
Cf. A365697.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(n-k+1,k) / (n-k+1).
Showing 1-5 of 5 results.

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