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.

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A366365 G.f. satisfies A(x) = (1 + x/A(x)^3)/(1 - x).

Original entry on oeis.org

1, 2, -4, 32, -240, 2064, -18816, 179264, -1762816, 17758976, -182342400, 1901196288, -20075427840, 214246524928, -2307200135168, 25039992254464, -273603550461952, 3007387399258112, -33230774508716032, 368915340555517952, -4112806343370539008
Offset: 0

Views

Author

Seiichi Manyama, Oct 08 2023

Keywords

Crossrefs

Cf. A346626, A349310, A349311, A349312, A349313, A349314, A366363, A366364, A366366.
Cf. A366358.

Programs

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

Formula

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

A366366 G.f. satisfies A(x) = (1 + x/A(x)^4)/(1 - x).

Original entry on oeis.org

1, 2, -6, 58, -574, 6402, -75878, 939290, -12000318, 157050178, -2094657926, 28368411194, -389079656446, 5393118559938, -75431624084838, 1063251390845338, -15088643098754942, 215396586102923138, -3091050571516120582, 44566089825496186170
Offset: 0

Views

Author

Seiichi Manyama, Oct 08 2023

Keywords

Crossrefs

Cf. A346626, A349310, A349311, A349312, A349313, A349314, A366363, A366364, A366365.
Cf. A366359.

Programs

  • PARI
    a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k-1, k)*binomial(4*k-1, n-k)/(5*k-1));

Formula

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(5*k-1,k) * binomial(4*k-1,n-k)/(5*k-1).

A364539 G.f. satisfies A(x) = 1 + x*A(x) + x^3*A(x)^5.

Original entry on oeis.org

1, 1, 1, 2, 7, 22, 62, 182, 583, 1928, 6358, 21063, 70888, 241889, 831634, 2874584, 9995579, 34966279, 122938956, 434062141, 1538378816, 5471697241, 19525345791, 69880082323, 250767909528, 902123110483, 3252793321513, 11753570922933, 42553831219830
Offset: 0

Views

Author

Seiichi Manyama, Jul 28 2023

Keywords

Crossrefs

Cf. A063019, A182454, A349311, A364522.
Cf. A023431, A071879, A215340.

Programs

  • PARI
    a(n) = sum(k=0, n\3, binomial(n+2*k, 5*k)*binomial(5*k, k)/(4*k+1));

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n+2*k,5*k) * binomial(5*k,k) / (4*k+1).

A365798 G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^4).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 253, 468, 848, 1618, 3433, 8009, 19384, 46264, 106369, 235179, 505955, 1079790, 2332555, 5166405, 11737860, 27086236, 62676956, 144074416, 327837356, 739787486, 1663922487, 3751649542, 8513640107, 19464624667
Offset: 0

Views

Author

Seiichi Manyama, Sep 19 2023

Keywords

Crossrefs

Cf. A063019, A182454, A349311, A364539, A364522.
Cf. A005708, A364523, A365732, A365733.
Cf. A002294, A365736.

Programs

  • PARI
    a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-k+1, n-5*k)/(n-k+1));

Formula

a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-k+1,n-5*k) / (n-k+1) = Sum_{k=0..floor(n/6)} binomial(n-k,5*k) * binomial(5*k,k) / (4*k+1).

A366647 G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^5.

Original entry on oeis.org

1, 1, 10, 100, 1120, 13600, 174352, 2322880, 31846720, 446387200, 6367988480, 92154502912, 1349572428800, 19963252142080, 297843703347200, 4476750466785280, 67724540010278912, 1030392038941573120, 15756269876770734080, 242027462112980172800
Offset: 0

Views

Author

Seiichi Manyama, Oct 15 2023

Keywords

Crossrefs

Partial sums give A349311.
Cf. A006319, A213282, A213336.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n+4*k-1, n-k)*binomial(5*k, k)/(4*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n+4*k-1,n-k) * binomial(5*k,k) / (4*k+1).
Previous Showing 11-15 of 15 results.

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