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.

A364592 G.f. satisfies A(x) = 1/(1-x) + x*(1-x)*A(x)^4.

Original entry on oeis.org

1, 2, 8, 49, 365, 3001, 26193, 238119, 2230151, 21368167, 208459419, 2063563791, 20675793627, 209277092776, 2136720896514, 21979879393677, 227582114799201, 2369983696546858, 24806423607475896, 260829829404493787, 2753744691645428399
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A014137, A188687.
Cf. A364594, A364596.

Programs

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

Formula

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

A364596 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^4.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 15, 36, 82, 191, 471, 1166, 2884, 7267, 18523, 47349, 121821, 315781, 822165, 2148811, 5641035, 14864295, 39287907, 104154066, 276899112, 737984583, 1971375679, 5277570860, 14156881590, 38045460023, 102421374775, 276174537027, 745822179831
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A364595, A364597.
Cf. A215340, A226974.
Cf. A364592, A364594.

Programs

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

Formula

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

A364593 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^3.

Original entry on oeis.org

1, 1, 2, 3, 7, 14, 36, 85, 228, 587, 1612, 4354, 12166, 33832, 95876, 271803, 779287, 2239584, 6483386, 18823945, 54932299, 160771540, 472322632, 1391323310, 4110685812, 12173949214, 36141795088, 107521223008, 320531857144, 957289637952, 2864055208772
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A110199, A364594.

Programs

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

Formula

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

A369688 G.f. satisfies A(x) = 1 + x*A(x) + x^2*(1-x)^3*A(x)^5.

Original entry on oeis.org

1, 1, 2, 4, 12, 36, 126, 442, 1644, 6172, 23801, 92731, 366688, 1462852, 5891808, 23898576, 97600556, 400844140, 1654818768, 6862550360, 28576414261, 119434041561, 500849380048, 2106740001442, 8886482895068, 37580609774876, 159303913630686
Offset: 0

Views

Author

Seiichi Manyama, Jan 28 2024

Keywords

Crossrefs

Cf. A227035, A346647, A364522, A364597.
Cf. A049130, A364594.

Programs

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

Formula

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