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).

A364594 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^4.

Original entry on oeis.org

1, 1, 2, 4, 11, 31, 98, 316, 1065, 3649, 12775, 45299, 162713, 590097, 2159015, 7957003, 29517141, 110116277, 412879256, 1555048142, 5880591163, 22319380999, 84992915958, 324634976440, 1243396473153, 4774504667881, 18376620653851, 70883537152927
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A110199, A364593.
Cf. A364592, A364596.

Programs

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

Formula

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

A364597 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^5.

Original entry on oeis.org

1, 1, 1, 2, 5, 11, 26, 71, 197, 540, 1521, 4401, 12826, 37597, 111385, 332861, 1000181, 3021071, 9174308, 27987989, 85712801, 263438881, 812394661, 2512807846, 7793552386, 24233089051, 75526196851, 235897169106, 738271145577, 2314825565700, 7270693111431
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A364595, A364596.

Programs

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

Formula

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

A364595 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^3.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 8, 15, 25, 50, 102, 193, 390, 815, 1645, 3385, 7141, 14893, 31196, 66309, 140752, 299043, 640367, 1373929, 2950006, 6360976, 13749865, 29753891, 64547097, 140329453, 305470485, 666084272, 1454920255, 3181946080, 6968134645, 15280422274
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A364596, A364597.

Programs

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

Formula

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