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.

Previous Showing 11-17 of 17 results.

A366456 G.f. A(x) satisfies A(x) = 1 + x + x/A(x)^(7/2).

Original entry on oeis.org

1, 2, -7, 56, -532, 5600, -62860, 737324, -8929726, 110811344, -1401640814, 18004922936, -234243536436, 3080152906096, -40870739065996, 546563064528906, -7358930622768977, 99672580921800656, -1357142384455626909, 18565841939010374736, -255054402946387767408
Offset: 0

Views

Author

Seiichi Manyama, Oct 10 2023

Keywords

Crossrefs

Cf. A112478, A364393, A364407, A364408, A364409, A366266, A366267, A366268, A366452, A366453, A366454, A366455.
Cf. A366402.

Programs

  • PARI
    a(n) = (-1)^(n-1)*sum(k=0, n, binomial(9*k/2-1, k)*binomial(n+7*k/2-2, n-k)/(9*k/2-1));

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366402.
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(9*k/2-1,k) * binomial(n+7*k/2-2,n-k) / (9*k/2-1).

A367641 G.f. A(x) satisfies A(x) = (1 + x)^2 + x*A(x)^4 / (1 + x)^3.

Original entry on oeis.org

1, 3, 10, 64, 504, 4368, 40208, 385728, 3813888, 38590208, 397648384, 4158436864, 44020882944, 470804670464, 5079479547904, 55217003536384, 604200374845440, 6649658071007232, 73560096496779264, 817467602640830464, 9121818467786162176
Offset: 0

Views

Author

Seiichi Manyama, Nov 25 2023

Keywords

Crossrefs

Cf. A367639, A367640.
Cf. A366267, A366272.

Programs

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

Formula

a(n) = Sum_{k=0..n} binomial(3*k+2,n-k) * binomial(4*k,k)/(3*k+1).
D-finite with recurrence 3*n*(5589*n-14914)*(3*n-1)*(3*n+1)*a(n) +(150903*n^4 -5939762*n^3 +21653157*n^2 -22049842*n +6856944)*a(n-1) +6*(-2312427*n^4 +15333754*n^3 -28367401*n^2 +6040114*n +14892656)*a(n-2) +24*(-3942141*n^4 +46541449*n^3 -199851671*n^2 +367766019*n -243569600)*a(n-3) -32*(n-5)*(8043984*n^3 -85808428*n^2 +305023231*n -361082892)*a(n-4) -384*(n-5)*(n-6)*(885234*n^2 -6808468*n +12951185)*a(n-5) -1536*(n-6)*(n-7)*(144699*n^2 -1203919*n +2337211)*a(n-6) -2048*(n-6)*(n-7)*(n-8)*(27819*n-74186)*a(n-7)=0. - R. J. Mathar, Dec 04 2023

A366557 G.f. A(x) satisfies A(x) = 1 + x + x^3*A(x)^4.

Original entry on oeis.org

1, 1, 0, 1, 4, 6, 8, 29, 84, 162, 360, 1074, 2808, 6444, 16464, 45629, 118244, 297450, 790184, 2138438, 5624136, 14778068, 39767024, 107287122, 286593800, 768920084, 2083170960, 5642886852, 15250029552, 41369986008, 112681853344, 306930498205, 836259756612
Offset: 0

Views

Author

Seiichi Manyama, Oct 13 2023

Keywords

Crossrefs

Cf. A137954, A366267, A366558.
Cf. A366594.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*k+1,n-3*k) * binomial(4*k,k)/(3*k+1).
a(n) = A366594(n) + A366594(n-1).

A366698 G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^4.

Original entry on oeis.org

1, 3, 13, 106, 1000, 10315, 112732, 1282262, 15021212, 179994093, 2195807684, 27179964798, 340514877488, 4309512389582, 55014793453124, 707582318505678, 9160219144520568, 119268621622902920, 1560830776582842660, 20519083242145870778, 270851956372499374728
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Cf. A366267, A366699, A366700.
Cf. A364621.

Programs

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

Formula

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

A366699 G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^4.

Original entry on oeis.org

1, 4, 19, 173, 1860, 21814, 271388, 3515330, 46906860, 640321565, 8899950644, 125524292790, 1791943900656, 25843064347685, 375956017001280, 5510454405453368, 81297696816798684, 1206334991431968912, 17991734573723974384, 269560224872407933010
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Cf. A366267, A366698, A366700.
Cf. A364624.

Programs

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

Formula

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

A366700 G.f. satisfies A(x) = (1 + x)^4 + x*A(x)^4.

Original entry on oeis.org

1, 5, 26, 258, 3093, 40333, 558368, 8051416, 119614784, 1818190754, 28142073936, 442026009500, 7027713442496, 112879991541322, 1828959159551328, 29857735697705720, 490633308020085056, 8108894353260093213, 134705809490320133544
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Cf. A366267, A366698, A366699.

Programs

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

Formula

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

A366677 G.f. satisfies A(x) = 1 + x^4 + x*A(x)^4.

Original entry on oeis.org

1, 1, 4, 22, 141, 973, 7112, 54040, 422552, 3377770, 27478568, 226753828, 1893462584, 15969598554, 135842638632, 1164075017512, 10039732285528, 87081507756245, 759128176746864, 6647475055207618, 58445784269830824, 515745587816906733
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Cf. A176697, A366676.
Cf. A366267, A366558.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(3*(n-4*k)+1,k) * binomial(4*(n-4*k),n-4*k)/(3*(n-4*k)+1).
Previous Showing 11-17 of 17 results.

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